Coding in a positioning system

ABSTRACT

Embodiments describe determining position by selecting a set of digital pseudorandom sequences. The magnitudes of the cross-correlation between any two sequences of the chosen set are below a specified threshold. A subset of digital pseudorandom sequences are selected from the set such that the magnitudes of the autocorrelation function of each member of the subset, within a specified region adjacent to the peak of the autocorrelation function, are equal to or less than a prescribed value. Each transmitter transmits a positioning signal, and at least a portion of the positioning signal is modulated with at least one member of the subset. At least two transmitters of the plurality of transmitters modulate respective positioning signals with different members of the subset of digital pseudorandom sequences.

TECHNICAL FIELD

The disclosure herein relates generally to positioning systems. Inparticular, this disclosure relates to a wide area positioning system.

BACKGROUND

Positioning systems like Global Positioning System (GPS) have been inuse for many years. In poor signal conditions, however, theseconventional positioning system can have degraded performance.

INCORPORATION BY REFERENCE

Each patent, patent application, and/or publication mentioned in thisspecification is herein incorporated by reference in its entirety to thesame extent as if each individual patent, patent application, and/orpublication was specifically and individually indicated to beincorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a wide area positioning system, under anembodiment.

FIGS. 2A and 2B (collectively FIG. 2) includes a table of preferentialGold codes of length 1023 in order of their −1 run length, under anembodiment.

FIG. 3 shows a plot of autocorrelation versus code phase for a preferredGold code, under an embodiment.

FIG. 4 includes a table of sets of Gold code pairs with longautocorrelation runs having amplitude −1, under an embodiment.

FIG. 5 shows a plot of autocorrelation magnitude versus code phase for apreferred Gold code pair, under an embodiment.

FIG. 6 shows a plot of transmitted symbol phase versus chip number for apreferred Gold code pair, under an embodiment.

FIG. 7 is a table of sets of preferential maximal length codes with lowcross-correlation values.

FIG. 8 is a block diagram of a synchronized beacon, under an embodiment.

FIG. 9 is a block diagram of a positioning system using a repeaterconfiguration, under an embodiment.

FIG. 10 is a block diagram of a positioning system using a repeaterconfiguration, under an alternative embodiment.

FIG. 11 shows tower synchronization, under an embodiment.

FIG. 12 is a block diagram of a GPS disciplined PPS generator, under anembodiment.

FIG. 13 is a GPS disciplined oscillator, under an embodiment.

FIG. 14 shows a signal diagram for counting the time difference betweenthe PPS and the signal that enables the analog sections of thetransmitter to transmit the data, under an embodiment.

FIG. 15 is a block diagram of the differential WAPS system, under anembodiment.

FIG. 16 shows common view time transfer, under an embodiment.

FIG. 17 shows the two-way time transfer, under an embodiment.

FIG. 18 is a block diagram of a receiver unit, under an embodiment.

FIG. 19 is a block diagram of an RF module, under an embodiment.

FIG. 20 shows signal up-conversion and/or down-conversion, under anembodiment.

FIG. 21 is a block diagram of a receiver system having multiple receivechains in which one of the receive chains can be used temporarily forreceiving and processing WAPS signals, under an embodiment.

FIG. 22 is a block diagram showing clock sharing in a positioningsystem, under an embodiment.

FIG. 23 is a block diagram of assistance transfer from WAPS to GNSSreceiver, under an embodiment.

FIG. 24 is a block diagram showing transfer of aiding information fromthe GNSS receiver to the WAPS receiver, under an embodiment.

FIG. 25 is an example configuration in which WAPS assistance informationis provided from a WAPS server, under an embodiment.

FIG. 26 is a flow diagram for estimating an earliest arriving path inh[n], under an embodiment.

FIG. 27 is a flow diagram for estimating reference correlation function,under an embodiment.

FIG. 28 is a flow diagram for estimating noise sub-space, under anembodiment.

FIG. 29 is a flow diagram for estimating noise sub-space, under analternative embodiment.

FIG. 30 is a flow diagram for estimating noise sub-space, under anotheralternative embodiment.

FIG. 31 is a flow diagram for estimating noise sub-space, under yetanother alternative embodiment.

FIG. 32 is a flow diagram for estimating noise sub-space, under stillanother alternative embodiment.

FIG. 33 is a block diagram of a reference elevation pressure system,under an embodiment.

FIG. 34 is a block diagram of the WAPS integrating the referenceelevation pressure system, under an embodiment.

FIG. 35 is a block diagram of hybrid position estimation using rangemeasurements from various systems, under an embodiment.

FIG. 36 is a block diagram of hybrid position estimation using positionestimates from various systems, under an embodiment.

FIG. 37 is a block diagram of hybrid position estimation using acombination of range and position estimates from various systems, underan embodiment.

FIG. 38 is a flow diagram for determining a hybrid position solution inwhich position/velocity estimates from the WAPS/GNSS systems are fedback to help calibrate the drifting bias of the sensors at times whenthe quality of the GNSS/WAPS position and/or velocity estimates aregood, under an embodiment.

FIG. 39 is a flow diagram for determining a hybrid position solution inwhich sensor parameters (such as bias, scale and drift) are estimated aspart of the position/velocity computation in the GNSS and/or WAPS unitswithout need for explicit feedback, under an embodiment.

FIG. 40 is a flow diagram for determining a hybrid position solution inwhich sensor calibration is separated from the individual positioncomputation units, under an embodiment.

FIG. 41 is a flow diagram for determining a hybrid position solution inwhich the sensor parameter estimation is done as part of the state ofthe individual position computation units, under an embodiment.

FIG. 42 shows the exchange of information between the WAPS and othersystems, under an embodiment.

FIG. 43 is a block diagram showing exchange of location, frequency andtime estimates between FM receiver and WAPS receiver, under anembodiment.

FIG. 44 is a block diagram showing exchange of location, time andfrequency estimates between WLAN/BT transceiver and WAPS Receiver, underan embodiment.

FIG. 45 is a block diagram showing exchange of location, time andfrequency estimates between cellular transceiver and WAPS receiver,under an embodiment.

FIG. 46 shows a parallel complex correlator architecture, under anembodiment.

FIG. 47 shows a 32-bit shift register implementation derived from two16-bit shift register primitives with parallel random access readcapabilities, under an embodiment.

FIG. 48 shows shift operation and readout operation rate, under anembodiment.

FIG. 49 shows a structure for an adder tree that implements a 1023×n-bitadder, under an embodiment.

FIG. 50 is a block diagram of session key setup, under an embodiment.

FIG. 51 is a flow diagram for encryption, under an embodiment.

FIG. 52 is a block diagram of the security architecture for encryption,under an alternative embodiment.

DETAILED DESCRIPTION

Systems and methods are described for determining the position of areceiver. The positioning system of an embodiment comprises atransmitter network including transmitters that broadcast positioningsignals. The positioning system comprises a remote receiver thatacquires and tracks the positioning signals and/or satellite signals.The satellite signals are signals of a satellite-based positioningsystem. A first mode of the remote receiver uses terminal-basedpositioning in which the remote receiver computes a position using thepositioning signals and/or the satellite signals.

The positioning system comprises a server coupled to the remotereceiver. A second operating mode of the remote receiver comprisesnetwork-based positioning in which the server computes a position of theremote receiver from the positioning signals and/or satellite signals,where the remote receiver receives and transfers to the server thepositioning signals and/or satellite signals.

A method of determining position of an embodiment comprises receiving ata remote receiver at least one of positioning signals and satellitesignals. The positioning signals are received from a transmitter networkcomprising a plurality of transmitters. The satellite signals arereceived from a satellite-based positioning system. The method comprisesdetermining a position of the remote receiver using one ofterminal-based positioning and network based positioning. Theterminal-based positioning comprises computing a position of the remotereceiver at the remote receiver using at least one of the positioningsignals and the satellite signals. The network-based positioningcomprises computing a position of the remote receiver at a remote serverusing at least one of the positioning signals and the satellite signals.

Further to the systems and methods for determining position, spreadingcodes and apparatus for wide area positioning are disclosed whichprovide improved structure to allow multipath mitigation for wide areapositioning systems. In particular, in addition to binary codes,quaternary and other non-binary spreading codes are described with verygood auto and cross correlation properties over limited code phaseranges. Non-binary codes allow higher data rates than binary codes, suchas those used in the Global Positioning System (GPS). These codes may beused in systems employing CDMA multiplexing, TDMA multiplexing,frequency offset multiplexing or any combination of these.

Systems and methods are described for determining position by selectinga set of digital pseudorandom sequences. The magnitudes of thecross-correlation function between any two sequences of the chosen setare below a specified threshold. A subset of digital pseudorandomsequences are selected from the set such that the magnitudes of theautocorrelation function of each member of the subset, within aspecified region adjacent to a peak of the autocorrelation function, areequal to or less than a prescribed value. Each transmitter of a networkof transmitters transmits a positioning signal, and at least a portionof the positioning signal is modulated in accordance with at least onemember of the subset. At least two transmitters of the network oftransmitters modulate respective positioning signals in accordance withdifferent members of the subset of digital pseudorandom sequences.

Furthermore, systems and methods are described for determining positionby selecting a set of digital pseudorandom sequences. The magnitudes ofthe autocorrelation function of any two sequences of the chosen set ofdigital pseudorandom sequences are below a specified threshold, within aregion adjacent to a peak of the autocorrelation function. A subset ofdigital pseudorandom sequences are selected from the set such that themagnitudes of the cross-correlation function of any pair of sequenceswithin the subset of digital pseudorandom sequences are equal to or lessthan a prescribed value. Each transmitter of a network of transmitterstransmits a positioning signal, and at least a portion of thepositioning signal is modulated in accordance with at least one memberof the subset. At least two transmitters of the network of transmittersmodulate respective positioning signals with different members of thesubset of digital pseudorandom sequences.

In the following description one may think of the autocorrelation (orcross-correlation) function as a set of time samples. With thisunderstanding, the terminology “region” means a set of consecutive timesamples of the function within a time interval specified by this region.The term “adjacent” means nearby. When it is stated that theautocorrelation function (or cross-correlation function) magnitudes arebelow a threshold within a region, what is meant is that each timesample of the autocorrelation function (or cross-correlation function)within this region has its magnitude below a threshold within a region.If a region is not specified then what is meant is every time sample.Depending upon the sequences employed, the cross-correlation functionmay be real or complex. The autocorrelation function is a real functionbut may be positive or negative. In most cases interest is in themagnitudes of such functions, and their polarities and or phases are ofless concern. Since the autocorrelation function is symmetric about itspeak value (which is positive), if such a function has magnitudes lessthan some threshold, within a region located above the positioncorresponding to the peak location, then there is necessarily asymmetrically disposed region situated below that of the peak locationfor which the autocorrelation magnitudes are also less than thisthreshold. This is in general not true for cross-correlation functions.

The following description includes use of the terminology that a signalis modulated in accordance with, or according to, a pseudorandom orother sequence. This means that the selection, or the changes, ofwaveforms transmitted during successive (typically small) intervals oftime are chosen in accordance with the successive elements of thesequence. Normally (but necessarily), a fixed mapping is made from thevalue of the sequence to the waveform selection or change. Examples ofembodiments include pseudorandom binary sequences whose values are usedto phase shift at regular intervals a carrier by either 0 or 180degrees. An alternative embodiment example is a pseudorandom quaternarysequence whose (one of four) values are used to phase shift a carrier byeither 0 degrees, 90 degrees, 180 degrees or 270 degrees. However, theembodiments herein are not limited to regular or irregular phase shifts,or regular or irregular intervals, but may apply to a variety ofmodulation methods, for example, frequency shifting, on-off keying,differential phase shift keying, pulse width modulation, etc. In someinstances, for reasons of brevity, terminology is used that apseudorandom sequence is used to “modulate” a signal. This nomenclatureis synonymous with the terminology that a signal is modulated“according” to such a sequence. From the context it should be clear ifthe modulation type is a binary phase reversal, or quaternary phaseshifting, or a more general modulation type. In the followingdescription, the terminologies sequence and codes are usedinterchangeably when referring to sequences used for pseudorandommodulation or spreading. This is distinct from data sequence, whichrefers to an information stream.

In the following description, numerous specific details are introducedto provide a thorough understanding of, and enabling description for,the systems and methods described. One skilled in the relevant art,however, will recognize that these embodiments can be practiced withoutone or more of the specific details, or with other components, systems,etc. In other instances, well known structures or operations are notshown, or are not described in detail, to avoid obscuring aspects of thedisclosed embodiments.

FIG. 1 is a block diagram of a positioning system, under an embodiment.The positioning system, also referred to herein as the wide areapositioning system (WAPS), or “system”, includes a network ofsynchronized beacons, receiver units that acquire and track the beaconsand/or Global Positioning System (GPS) satellites (and optionally have alocation computation engine), and a server that comprises an index ofthe towers, a billing interface, a proprietary encryption algorithm (andoptionally a location computation engine). The system operates in thelicensed/unlicensed bands of operation and the beacons transmitproprietary waveforms for the purposes of location and navigationpurposes. The WAPS system can be used in conjunction with otherpositioning systems for better location solution or the WAPS system canbe used to aid other positioning systems

In the context of this document, a positioning system is one thatlocalizes one or more of latitude, longitude and altitude coordinates.Whenever the ‘GPS’ is referred to, it is done so in the broader sense ofGNSS (Global Navigation Satellite System) which may include otherexisting satellite positioning systems such as Glonass as well as futurepositioning systems such as Galileo and Compass/Beidou.

The WAPS of an embodiment includes multiple towers broadcastingsynchronized positioning signals to mobile receivers as described indetail herein. The towers of an embodiment are terrestrial, but theembodiment is not so limited. A significant problem that occursparticularly in terrestrial systems, especially ones that operate inurban environments, is the presence of multipath. In these situations,the mobile receiver may receive a multiplicity of signals from atransmitter, corresponding to a multiplicity of direct and reflectedpaths. The range of delays, sometimes called the delay spread, istypically constrained by geometric situations. For example, a delayspread of 1 microsecond corresponds to a maximum differential pathlength of 300 meters, and a spread of 5 microseconds to 1499 meters.

Typical WAPS use coded modulation, called spread spectrum modulation, orpseudonoise (PN) modulation, to achieve wide bandwidth. In such a systema carrier signal is modulated by a wideband modulated signal (typicallya digital modulation), and such wide bandwidth permits accuratepositioning through use of time-of-arrival measurement methods. Themobile receiver processes such signals with a de-spreading device,typically a matched filter or a series of correlators. Such a receiverproduces a waveform, termed a cross-correlation function, which ideallyhas a narrow, strong peak surrounded by lower level energy. The time ofarrival of the peak represents the time of arrival of the transmittedsignal at the mobile. Performing this operation on a multiplicity ofsignals from a multiplicity of towers, whose locations are accuratelyknown, allows determination of the mobile's location via trilaterationalgorithms.

Assuming use of a matched filter to process a received spread spectrumsignal, when multipath is present, the matched filter output provides aseries of overlapping sharp pulses of varying amplitudes, delays andphases. The mobile receiver attempts to estimate the time of arrival ofthe earliest such pulse. A variety of algorithms may be used for thispurpose, such as leading edge location algorithms, MUSIC algorithm,minimum mean square estimation algorithms, etc.

A problem that arises, however, is that the energy surrounding the peaktypically contains a series of subsidiary peaks, or “sidelobes”. Thespecification of the structure of such sidelobes in an ideal situation(i.e. no noise or multipath) is provided by a function called the“autocorrelation function.” In multipath environments, these subsidiarypeaks may be confused with a weak early signal arrival. For example, inthe GPS system, for the C/A civilian codes, certain binary spreadingcodes, called “Gold Codes”, are used, which are of frame length 1023symbols, or “chips”. An ideal matched filter receiving such a Gold codeproduces a set of sidelobes of amplitude − 65/1023 times the peakamplitude, 63/1023 times the peak amplitude and − 1/1023 times the peakamplitude. Thus the magnitude of the largest sidelobe is approximately0.06 times the peak amplitude or −24 dB. Typically these large amplitudesidelobes may be adjacent to or close to the peak amplitude of theautocorrelation function. Improved multipath estimation may be achievedby choosing codes that have a large region about the peak of theautocorrelation where (for the length 1023 case) the sidelobe value is −1/1023 times the peak. This is referred to as the −1 run length.Specifically, for this case, the −1 run length is defined as the numberof consecutive chips on one side of the autocorrelation peak, ofamplitude − 1/1023 times the peak. An embodiment described herein is thechoice of a set of Gold Codes with the largest −1 run length. Otherclasses of code sets may be used in various alternative embodiments, asdescribed in detail herein.

For the purpose of simplicity of description, the primary focus hereinis upon the circular, or “periodic” autocorrelation function, whichstrictly speaking applies to the case in which transmitted codesequences, such as the above Gold codes, are repeated more than once.Hence the discussion of autocorrelations and cross-correlations is,strictly speaking, synonymous with circular cross correlation andcircular autocorrelation. However, the application and benefits of theideas of this description are also applicable to the situations ofnoncircular, or “aperiodic” correlations, especially when the concernsare focused upon performance near the peak of the output of the matchedfilter (or set of correlator). This is the case since near the peakoutput of the matched filter the aperiodic autocorrelation function isnearly equal to the circular autocorrelation function. Similarly theaperiodic cross-correlation function may be similar to the circularaperiodic cross-correlation function when the two sequences beingcross-correlated have their start epochs nearly aligned.

The above discussion of a spread spectrum modulated signal described asignal suitable for use in positioning. However, it is generally thecase that signals transmitted from the various transmitters include datanecessary for the position location calculation. Such data mightinclude, for example, the geographical location of the transmitters,times of transmission, environmental data, etc. Another set of suchlower speed data might include a sequence used for the purpose ofoverall signal synchronization. In either case this data is generallytransmitted at a much lower rate than the bandwidth of the spreadingsignal. Often this data is further modulated on top of the spreadspectrum modulated signal that is used for positioning, and often thedata epochs are aligned with epochs of the spread spectrum modulation,for example the beginning of the pseudorandom frames. Although it isoften the case that both the spread spectrum modulation and the datamodulation are used to phase shift a signal carrier, it is notnecessarily the case, and the embodiments herein are not so limited.Furthermore, it may be the case that a portion of a transmitted signalmay include only a spread spectrum modulated carrier without anyadditional data and another portion of a transmitted signal may includea carrier modulated by both a spread spectrum signal and data. It alsomay be the case that both modulations may be present in differentportions of the transmitted signal, but different pseudorandom sequencesmay be used in the different portions of the transmission. In thefollowing discussion when terms such as data, data rate, datamodulation, data bits, and information bits are used, it is generallythe case that such terminology refers to the data type as discussed inthis paragraph, as contrasted with the spreading modulation.

As described in detail below, an embodiment includes the use ofquadraphase or higher order coded modulation for the transmittedmodulation. For a system that uses BPSK data modulation and BPSKspreading, it is sufficient to choose good −1 run length sequences formultipath mitigation. When quadrature spreading is used, it is necessarynot only to have good −1 run length for the various tributaries used inconstructing the quadraphase code, but also to have very goodcross-correlation properties between the codes of the tributaries forcode offsets consistent with the −1 run length. An alternativeembodiment of a method described herein includes the choosing of pairsor larger sets of codes.

Many WAPS use binary coded modulation, as the spreading method. Anembodiment produces quaternary coded modulation constructed in a mannerto minimize the effects of multipath, as described above. Other higherorder coding modulations are also disclosed, with similar advantageswith respect to multipath mitigation.

In binary coded modulations the transmitting source produces at anyinstance one of two waveforms corresponding to one of two symbols,typically represented as −1 and +1, or 0 and 1. The waveforms typicallyare biphase coded, meaning that the signal is either a signal istransmitted or its inverse is transmitted, by phase inverting thecarrier. It is possible to use frequency shift keying, amplitude shiftkeying, etc. to transmit a binary coded signal.

In quaternary coded modulation the transmitter source transmits at anytime one of four possible symbols, which may be denoted A, B, C, and D.An embodiment includes a transmitter that maps these four symbols intoone of four possible phases, producing a quadraphase modulated signal.One method of producing such a quadraphase modulated spreading signal isto use two Gold Codes that modulate inphase and quadrature components ofthe transmitted carrier. The transmitted signal at any instance of timeis again one of four symbols, corresponding to four carrier phases. Thenumber of possible symbols transmitted at any one time is sometimescalled the alphabet size. Hence, in the quaternary case, the alphabetsize is 4. Any alphabet size is possible; however the use of a smallalphabet size may result in reduced system complexity. Well knownpseudorandom sequences exist, having good autocorrelation and crosscorrelation properties, in which the element of each sequence is one ofM possible values. Again this value M is referred to as the alphabetsize of the sequence. In transmitting signals in accordance with such asequence there is a mapping of each sequence element value to anappropriate waveform. For example, a sequence may have an alphabet sizeof 16, and one possible mapping would be a mapping of each of the 16possible values to one of 16 possible phase shifted exponentials. It isnot necessary to construct higher order sequences, from lower orderones, such as Gold codes—they may be constructed directly. However,exemplary illustrations now provided illustrate such constructions.

The use of quaternary coding of data, rather than binary coding of data,enables the data rate transmitted by the transmitter to be doubledwithout affecting the signal structure. For example, if the code lengthis N symbols, then the entire spreading sequence of N transmitted(quaternary) symbols may be further phase shifted by 0, 90, 180 or 270degrees in order to transmit 2 bits of data per code period, rather thanone bit which is the case for biphase coding.

A further advantage of quarternary coding of the spreading signal isthat the method provides a means of discriminating a signal from anothertransmitter having the same code and overlapping in time. Thetransmitted sequence of symbols from one transmitter can be representedas A+jB where A is a particular Gold Code (for example) and B is anotherGold code, and j represents 90° phase shift. The second transmitter cantransmit A-jB. Both transmitters are transmitting quaternary symbols ina similar manner but the relationship between the inphase and quadraturecomponents is altered and is easily determined by a receiver.

Higher order spreading modulation can be constructed in a variety ofways. For example, a code may be constructed that has alphabet size 8.Each symbol of the code may be mapped into a phase shift of the carrierby an amount k×γi/4, k=0, 1, . . . , 7. Alternatively, each symbol maybe mapped to a combination of amplitude and phase shifts. In thisexample of alphabet size 8, the transmitter may compute the codesequence and the mapping (3 bit word to transmitted symbol) on the fly,or it may store the full sequence or the entire frame of symbols andread such data out from memory as needed.

In all of the scenarios described above the performance of the system isthe same from the standpoint of measurement of range, assuming the sametransmitted and received energy, the same spreading symbol shape, andthe same spreading symbol rate. However, there is less energy perinformation bit if more than one information bit is transmitter per PNframe length. In many terrestrial wide area positioning systems, thereis good received signal energy, and hence this limitation may be minor.

FIGS. 2A and 2B (collectively referred to as FIG. 2) include a table 200of preferential Gold codes of length 1023 in order of their −1 runlength, under an embodiment. In more general cases than describedherein, the “−1 run length” means the number of consecutive code phasesfollowing the correlation peak which have values +/−1 times the peakvalue divided by the code length. Each of the Gold codes is constructedfrom the same pair of maximal length codes, with the different Goldcodes distinguished by the delay, or code phase, difference between thepair. Table 200 also includes the initial fill of the second PN code'sshift register as an alternative to the delay, since the initial fill istypically more closely related to how the sequence will be generated.The fill of the first PN code in the table is always equal to all 1's.The fill of the second PN code is as specified in the table. The fillread from left to right represents the first 10 outputs of the second PNgenerator. The fill is placed in the shift register from the end of theshift register back to the beginning. PN Code 1 has feedback taps [3,10]and code 2 has taps [2,3,6,8,9,10]. The best code displayed in table 200has a run of 25 (one each side of the autocorrelation peak). In additionto the codes shown in table 200, each of the individual maximal lengthcodes, i.e. code 1 and code 2 by itself, may also be used to augment thecodes of table 200, since they may be considered part of the Gold codeset (since they share the Gold code set cross-correlation propertieswith the other members). Furthermore, these maximal length codes have(circular) autocorrelation functions that are −1, except for thecorrelation peak. If these codes were included in the codes of table200, their −1 run length would be 1022, and hence they would be placedat the head of the list.

It should be noted that other pairs of maximal length PN codes may beused to construct sets of Gold codes with good −1 run lengths. The codepairs selected herein are for illustrative purposes. Furthermore, tablesmay be constructed in a similar manner for other code lengths for whichGold codes exist. In addition other sets of codes, rather than Gold codesets may be selected and subsets of such sets may be selected for good−1 run lengths. These variations are described in detail herein.

FIG. 3 shows a plot 300 of autocorrelation versus code phase for apreferred Gold code, under an embodiment. More specifically, the plot300 shows the central portion of an autocorrelation of the first entryof table 200 (preferential order is 1, delay between codes is 853,equivalent fill is 1000100001, −1 sidelobe run length is 25), which hasa −1 run length of 25.

A quaternary coded signal may be constructed by employing two Gold codesin quadrature, as described in detail above. In this case, theautocorrelation function will have four terms corresponding to theindividual autocorrelations of the two Gold codes and the crosscorrelations between the Gold codes. That is, if the constituent goldcodes are called g and h, then the overall code may be represented asg+jh. The autocorrelation then becomes g⊗g+h⊗h−jg⊗h+jh⊗g, where ⊗ meanscorrelation, and we note that when correlating two complex quantities,the second such quantity is complex conjugated. The last two terms inthis overall autocorrelation are the cross correlations. In order toconstruct a good quaternary code with large −1 run length it is thusnecessary not only to utilize Gold codes that have good individual −1run length, but also to have their cross correlations contributenegligibly in the vicinity of the same code phase interval in which theautocorrelation function of the individual Gold codes have value −1. Theinterval of low cross correlation values is referred to herein as across-correlation run. A choice of pairs of such codes can be done bytaking advantage of the fact that one can choose the relative code phasebetween the Gold codes in order to achieve good cross correlationperformance over the code phase interval of interest. An embodimentincludes a set of pairs of Gold codes determined in this manner byexamining all pairs of Gold codes in table 200 and all relative codephases between such pairs. It should be noted that a correlationoperation for quaternary codes (or any codes higher than binary)involves multiplying by the complex conjugate of the idealized receivedsignal.

FIG. 4 includes a table 400 of sets of Gold code pairs that may be usedto construct a quadrature code having long −1 run length, under anembodiment. The delay in the third column is that applied to Gold code 2in order to achieve an overall autocorrelation of the quadraturemodulated signal with a long −1 run length as shown in the fourthcolumn. Note that in this case if the constituent Gold code sequenceshave amplitudes +/−1, the overall autocorrelation during the runs hasamplitude −2 and the peak of the autocorrelation is 2046. The run lengthdefinition is consistent with the prior definition since −1 times thepeak value divided by the code length equals −1 times 2046/1023=−2. FIG.5 shows a plot 500 of autocorrelation magnitude versus code phase for apreferred Gold code pair, under an embodiment. More specifically, theplot 500 shows the central portion of the magnitude of theautocorrelation of the second entry of table 500 (Gold code 1 (PN delay)is 714, Gold code 2 (PN2 delay) is 456, inserted delay (to code 2) tocenter cross correlation run is 343, total cross correlation run is 37),which implies a −1 run length of 18 on either side of theautocorrelation peak. The magnitude has been divided by two in order tocompare this with plot 300 (FIG. 3). The insertion of the proper delaybetween the constituent Gold codes is critical in constructing aquaternary code with good autocorrelation properties because otherwisethe autocorrelation function about the peak may have large close-insidelobes.

FIG. 6 shows a plot 600 of transmitted symbol phase versus chip numberfor a preferred Gold code pair, under an embodiment. More specifically,plot 600 shows a sample portion of the transmitted symbol phase angle indegrees versus chip number for the second entry of table 400 (Gold code1 (PN delay) is 714, Gold code 2 (PN2 delay) is 456, inserted delay tocenter cross correlation run is 343, total cross correlation run is 37).The plot 600 shows a sequence of four phases, +/−45 degrees and +/−180degrees, representing the quaternary code. It is noted that thetransmitter itself need only store the sequence of phase angles, orsymbol designations (e.g. A, B, C, and D) rather than implement the codeusing shift registers, or the like.

Although the description herein focuses upon Gold codes, the ideasextend to other classes of codes. A number of code classes, suitable foruse in spread spectrum multiplexing may initially be selected. Forexample, such sets may include Kasami codes, Bent Codes, and Gold-likecodes, but the embodiments are not so limited. These sets generally havegood (aperiodic) cross correlation properties between pairs of members.Then, following an embodiment, a subset of such codes may be selectedwith circular autocorrelations having long −1 run length. Similarly,sets of codes having good cross correlation properties may be selectedhaving alphabet size greater than two, for example quaternary, octonary,etc. Then subsets of these may be selected for good circularautocorrelation properties.

In the description herein a primary measure of performance is the −1 runlength of the autocorrelation function. This corresponds to the lengthof the autocorrelation function on either side of its peak having value−1 times the peak value/code length. However, a further embodimentherein selects a subset of codes with autocorrelation magnitude levelsno greater than a threshold value A, within a specified region about thepeak autocorrelation value. This is termed the A run length. As before,the set of sequences is chosen such that the maximum magnitude of thecross-correlation function between any pair of codes is below aspecified value. Next a subset of such a set of codes is selected suchthat for each of such subset members the autocorrelation functionmagnitudes, within a specified location region near the peak, is lessthan or equal to the value A. For the prior discussion of the binary andquaternary Gold codes A had value 1, assuming that the Gold codesequences have values +1 and −1.

In another embodiment, a set of codes is initially selected with goodautocorrelation properties over a range about its peak location. Asubset of such codes is then selected in which the pairwisecross-correlation magnitude between members (optionally over a range ofcode phases) is less than a specified threshold C. This may apply tobinary codes or codes with larger alphabets (e.g. quaternary). Forexample, consider the set of maximal length sequences of a given size,for example 2047. For this case there are 176 such codes. Of course,each has very good autocorrelation properties, with −1 run length 1022.The cross-correlation between members will vary significantly. FIG. 7 isa table 700 of code subsets selected to have bounded cross correlationmagnitudes between members, under an embodiment. Better performance isachieved by limiting the size of the subsets. For example, for codelength 2047, maximum cross-correlation magnitude of 65 may be achievedif the set size is limited to 3, and maximum cross-correlation magnitudeof 129 may be achieved if the set size is limited to 10.

In an embodiment, the codes described herein are used to modulate acarrier and hence create a positioning signal. The code may be repeatedone or more times. Such a signal may include other signaling elements inaddition to, or instead of, such positioning signals. For example, asdescribed herein, a portion of such a signal may include positioningsignals by themselves, another portion may include the positioningsignals further modulated by a lower speed data sequence, and otherportions of the signal may include other signal elements with nospreading code at all. In yet another embodiment the transmitted signalis not continuous, but is transmitted as a set of bursts, in a timedivision multiplexed manner. An individual transmitter may use the samecode or codes in each burst, or these codes may vary from one burst tothe next. The embodiments herein apply to all such situations when atleast one portion of such a transmission incorporates a pseudorandom orspreading code selected in the manner prescribed herein.

In an embodiment, selected code sets may have sequence lengths that aretruncated to less than a standard sequence length, or extended to agreater length. For example, rather than using a standard Gold code oflength 2047, a code length of 2046 may be used instead by deleting onecode element. This may allow simpler implementation in situations inwhich multiple lengths are employed. For example, a system can operateat one rate, a first rate, and in other situations operate at a secondrate that is twice the first rate. If a code length of 1023 is used inthe first instance, then the system should be operated with a codelength of 2046 in the second instance in order to maintain the sameframe (that is, sequence) duration. In yet another embodiment, differenttransmitters using codes selected according to the embodiments describedherein transmit signals with slightly different carrier frequencies.

Waps Systems and Methods

FIG. 8 is a block diagram of a synchronized beacon, under an embodiment.With reference to FIG. 8 as well as FIG. 1, the synchronized beacons ofan embodiment, also referred to herein as beacons, form a CDMA network,and each beacon transmits a signal in accordance with a Pseudo RandomNumber (PRN) sequence with good cross-correlation properties such as aGold Code sequence with a data stream of embedded assistance data.Alternatively, the sequences from each beacon transmitter can bestaggered in time into separate slots in a TDMA format.

In a terrestrial positioning system, one of the main challenges toovercome is the near-far problem wherein, at the receiver, a far-awaytransmitter will get jammed by a nearby transmitter.

To address this issue, beacons of an embodiment use a combination ofCDMA, TDMA techniques, and frequency offset techniques. Such a system istermed a hybrid multiplexing system since it is not one of these methodsalone, but a combination. As an example, local transmitters may useseparate time slots (and optionally different codes (CDMA)) to alleviatethe near-far problem. Transmitters somewhat further afield would beallowed to use the same time slots while using different CDMA codes,and/or frequency offsets. This allows wide-area scalability of thesystem. The time slotting can be deterministic for guaranteed near-farperformance or randomized to provide good average near-far performance.As indicated herein, the carrier signal can also be offset by a smallfrequency difference (for example, on the order of the Gold code repeatfrequency) to improve cross-correlation performance of the codes andhence address ‘near-far’ issues. When two towers use the same time slotbut different codes, and or offset frequencies, the cross-correlation inthe receiver can be further rejected by using interference cancellationof the stronger signal before detecting the weaker signal. In the hybridpositioning systems described herein sophisticated planning methods areused to assign to each transmitter combinations of time slots, CDMAcodes, and frequency offsets so as to maximize overall systemperformance. The number of combinations of these parameters is limitedin order to allow signal acquisition time by a receiver to be apractical value.

Additionally, the beacons of an embodiment can use a preamble includingassistance data or information can be used for channel estimation andForward Error Detection and/or Correction to help make the data robust.The assistance data of an embodiment includes, but is not limited to,one or more of the following: precise system time at either the risingor falling edge of a pulse, or a specified signal epoch, of thewaveform; Geocode data (Latitude, Longitude and Altitude) of the towers;geocode information about adjacent towers and index of the sequence usedby various transmitters in the area; clock timing corrections for thetransmitter (optional) and neighboring transmitters; local atmosphericcorrections (optional); relationship of WAPS timing to GNSS time(optional); indication of urban, semi-urban, rural environment to aidthe receiver in pseudorange resolution (optional); and, offset from baseindex of the PN sequence or the index to the Gold code sequence. In thetransmit data frame that is broadcast, a field may be included thatincludes information to disable a single or a set of receivers forsafety and/or license management reasons.

The transmit waveform timing of the transmissions from the differentbeacons and towers of an embodiment are synchronized to a common timingreference. Alternatively, the timing difference between thetransmissions from different towers should be known and transmitted. Theassistance data is repeated at an interval determined by the number andsize of the data blocks, with the exception of the timing message whichwill be incremented at regular intervals. The assistance data may beencrypted using an encryption algorithm. The spreading code may also beencrypted for additional security. The signal is up-converted andbroadcast at the predefined frequency. The end-to-end delay in thetransmitter is accurately calibrated to ensure that the differentialdelay between the beacons is less than approximately 3 nanoseconds.Using a differential WAPS receiver at a surveyed location listening to aset of transmitters, relative clock corrections for transmitters in thatset can be found.

The tower arrangement of an embodiment is optimized for coverage andlocation accuracy. The deployment of the towers will be arranged in sucha way as to receive signals from 3 or more towers in most of thelocations within the network and at the edge of the network, such thatthe geometric dilution of precision (GDOP) in each of these locations isless than a predetermined threshold based on the accuracy requirement.Software programs that do RF planning studies will be augmented toinclude the analysis for GDOP in and around the network. GDOP is afunction of receiver position and transmitter positions. One method ofincorporating the GDOP in the network planning is to set up anoptimization as follows. Function to be minimized is volume integral ofthe square of GDOP over the coverage volume. The volume integration iswith respect to the (x, y, z) coordinates of the receiver position. Theminimization is with respect to the n transmitter position coordinates(x₁, y₁, z₁), (x₂, y₂, z₂), . . . (x_(n), y_(n), z_(n)) in a givencoverage area subject to the constraints that they are in the coveragevolume: x_(min)<x<x_(max), y_(min)<y<y_(max), z_(min)<z<z_(max) for i=1,. . . , n with x_(min), y_(min) and z_(min) being the lower limits andwith x_(max), y_(max) and z_(max) being the upper limits of the coveragevolume. The function to be minimized can be written as

${f\left( {x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots \mspace{14mu} n}} \right)} = {\underset{{x \in {({{xl},{xu}})}},{y \in {({{yl},{yu}})}},{z \in {({{zl},{zu}})}}}{\int{\int\int}}{{GDOP}^{2}\left( {x,y,z,x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots \mspace{14mu} n}} \right)}}$

Additionally, the function to be minimized may be weighted according tothe importance (i.e. performance quality required) of the coverageregion R_(j).

${f\left( {x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots \mspace{14mu} n}} \right)} = {\sum\limits_{j}{W_{j}\underset{x,y,{z \in R_{j}}}{\int{\int\int}}{{GDOP}^{2}\left( {x,y,z,x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots \mspace{14mu} n}} \right)}}}$

An additional constraint on the tower coordinate locations can be basedon location of already available towers in the given area. Thecoordinatization of all coordinates can typically be done in local levelcoordinate system with average east as positive x, average north aspositive y and average vertical up as positive z. The software whichsolves the above constrained minimization problem will output optimizedtransmitter positions x1,y1,z1, x2,y2,z2, . . . (xn,yn,zn) that wouldminimize the function f.

$\arg \; {\min\limits_{x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots \mspace{14mu} n}}\left( {f\left( {x_{i},y_{i},{z_{i};{i = 1}},2,{\ldots \mspace{14mu} n}} \right)} \right)}$

This technique can be applied for both wide area networks (like in acity) or in a local deployment (like in a mall). In one exampleconfiguration, the network of transmitters is separated by a distance ofapproximately 30 km in a triangular/hexagonal arrangement around eachmetropolitan area. Each tower can radiate via a corresponding antenna upto a maximum power in a range of approximately 20 W to 1 kW EIRP. Inanother embodiment, the towers can be localized and can transmit atpower levels as low as 1 W. The frequency bands of operation include anylicensed or unlicensed band in the radio spectrum. The transmit antennaof an embodiment includes an omni-directional antenna, or multipleantennas/arrays that can help with diversity, sectoring etc.

Adjacent towers are differentiated by using different sequences withgood cross-correlation properties to transmit or alternatively totransmit the same sequences at different times. These differentiationtechniques can be combined and applied to only a given geographicalarea. For instance the same sequences could be reused over the networksin a different geographical area.

Local towers can be placed in a given geographical area to augment thewide area network towers of an embodiment. The local towers, when used,can improve the accuracy of the positioning. The local towers may bedeployed in a campus like environment or, for public safety needs,separated by a distance in a range of few 10s of meters up to a fewkilometers.

The towers will preferably be placed on a diversity of heights (ratherthan on similar heights) to facilitate a better quality altitudeestimate from the position solution. In addition to transmitters atdifferent latitude/longitude having different heights, another method toadd height diversity to the towers is to have multiple WAPS transmitters(using different code sequences) on the same physical tower (withidentical latitude and longitude) at different heights. Note that thedifferent code sequences on the same physical tower can use the sameslots, because transmitters on the same tower do not cause a near-farproblem.

WAPS transmitters can be placed on pre-existing or new towers used forone or more other systems (such as cellular towers). WAPS transmitterdeployment costs can be minimized by sharing the same physical tower orlocation.

In order to improve performance in a localized area (such as, forexample, a warehouse or mall), additional towers can be placed in thatarea to augment the transmitters used for wide area coverage.Alternatively, to lower costs of installing full transmitters, repeaterscan be placed in the area of interest.

Note that the transmit beacon signals used for positioning discussedabove need not be transmitters built exclusively for WAPS, but can besignals from any other system which are originally synchronized in timeor systems for which synchronization is augmented through additionaltiming modules. Alternately, the signals can be from systems whoserelative synchronization can be determined through a reference receiver.These systems can be, for example, already deployed or newly deployedwith additional synchronization capability. Examples of such systems canbe broadcast systems such as digital and analog TV or MediaFlo.

When the WAPS network is configured, some transmit locations may bebetter than some others in the network (height of the beacon aboveclutter, power levels) either determined by design or by fieldmeasurements. Such beacons can be identified to the receivers eitherdirectly or indirectly or by encoding data bits which indicate the“quality” of the beacon which the receivers can then use to weight thesignal received from such beacons.

FIG. 9 is a block diagram of a positioning system using a repeaterconfiguration, under an embodiment. The repeater configuration comprisesthe following components:

1) A common WAPS receive antenna (Antenna 1)

2) An RF power amplifier and a splitter/switch connects to various WAPStransmitter antennas (Local Antennas 1-4).

3) WAPS User Receiver

Antennal receives, amplifies and distributes (switches) the compositesignal to Local Antennas 1-4. The switching should be done (preferably)in a manner such that there is no overlap (collision) of transmissionsfrom different repeaters at the user receiver. Collision oftransmissions can be avoided through the use of guard intervals. Theknown cable delays from the switch to the transmit antenna should becompensated either by adding delays at therepeater-amplifier-transmitter to equalize the overall delay for alllocal repeaters or by adjusting the estimated time of arrival from aparticular repeater by the cable delay at the user-receiver. When TDMAis used in the wide area WAPS network, the repeater slot switching rateis chosen such that each wide area slot (each slot will contain one widearea WAPS tower) occurs in all repeater slots. One example configurationwould use the repeater slot duration equal to a multiple of the widearea TDMA frame duration. Specifically, if the wide area TDMA frame is 1second, then the repeater slots can be integer seconds. Thisconfiguration is the simplest, but is suitable only for deployment in asmall, limited area because of requirement of RF signal distribution oncables. The user WAPS receiver uses time-difference of arrival whenlistening to repeater towers to compute position and works under astatic (or quasi static) assumption during the repeater slotting period.The fact that the transmission is from a repeater can be detectedautomatically by the fact that each WAPS tower signal shows the sametiming difference (jump) from one repeater slot to the next one.

FIG. 10 is a block diagram of a positioning system using a repeaterconfiguration, under an alternative embodiment. In this configurationeach repeater comprises a WAPS repeater-receiver and an associatedcoverage-augmentation WAPS transmitter with local antenna (which can beindoors, for example). The WAPS repeater receiver should be able toextract WAPS system timing information as well as WAPS data streamcorresponding to one wide area WAPS transmitter. The WAPS system timingand data corresponding to one wide area WAPS transmitter are passed tothe corresponding local area WAPS transmitters which can thenre-transmit the WAPS signal (for example, using a different code and thesame slot). The transmitter will include additional data in itstransmission such as latitude, longitude and altitude of the localantenna. In this configuration, the WAPS user receiver operation (rangemeasurement and position measurement) can be transparent to the factthat the signals are coming from repeaters. Note that the transmitterused in the repeater is cheaper than a full WAPS beacon in that it doesnot need to have a GNSS timing unit to extract GNSS timing.

Depending on the mode of operation of the receiver unit, eitherterminal-based positioning or network-based positioning is provided bythe system. In terminal based positioning, the receiver unit computesthe position of the user on the receiver itself. This is useful inapplications like turn-by-turn directions, geo-fencing etc. In networkbased positioning, the receiver unit receives the signals from thetowers and communicates or transmits the received signal to a server tocompute the location of the user. This is useful in applications likeE911, and asset tracking and management by a centralized server.Position computation in the server can be done in near real time orpost-processed with data from many sources (e.g., GNSS, differentialWAPS etc.) to improve accuracy at the server. The WAPS receiver can alsoprovide and obtain information from a server (similar, for example, to aSUPL Secure User PLane server) to facilitate network based positioning.

The towers of an embodiment maintain synchronization with each otherautonomously or using network-based synchronization. FIG. 11 shows towersynchronization, under an embodiment. The following parameters are usedin describing aspects of synchronization: System Tx time=t_(wAPS-tx);Absolute time reference=t_(WAPS_abs); TimeAdjustment=Δ_(system)=t_(WAPS-tx)−t_(WAPS_abs). Note that it is notessential to synchronize WAPS system time to an absolute time reference.However, all WAPS transmitters are synchronized to a common WAPS systemtime (i.e. relative timing synchronization of all WAPS transmitter).Timing corrections of each transmitter relative to WAPS system time (ifany) should be computed. The timing corrections should be made availableto the receivers either directly through over the air WAPS assistancetransmission or through some other communication means. The assistancecan be delivered, for example, to the WAPS receiver through a cellular(or other) modem or through a broadcast data from a system (such asIridium or digital TV or MediaFlo or broadcast channels of cellularsystems). Alternatively, the timing correction can be sent to the serverand used when computing position at the server. A description of towersynchronization of an embodiment follows.

Under network based synchronization, the towers synchronize with eachother in a local area. The synchronization between towers generallyincludes transmission of a pulse (which can be modulated using any formof modulation onto a carrier and/or spread using a spreading code forbetter time resolution which in turn modulates a carrier) andsynchronizing to the pulse edge on the receiver, as described in detailherein.

In the autonomous synchronization mode of an embodiment, the towers aresynchronized using a local timing reference. The timing reference can beone of the following, for example: GPS receivers; highly accurate clocksources (e.g., Atomic); a local time source (e.g., GPS disciplinedclock); and, any other network of reliable clock sources. Use of signalsfrom XM satellite radio, LORAN, eLORAN, TV signals etc. which areprecisely time synchronized can be used as a coarse timing reference forthe towers. As an example in one embodiment, FIG. 12 is a block diagramof a PPS pulse source from a GPS receiver being used to discipline anaccurate/stable timing source such as a Rubidium, Caesium or a hydrogenmaster, under an embodiment. Alternatively, a GPS disciplined Rubidiumclock oscillator can be used, as shown in FIG. 13.

With reference to FIG. 12, the time constant of the PLL in the accurateclock source is set to a large enough number (e.g., in the range of0.5-2 hours) which provides for better short term stability (orequivalently, filtering of the short term GPS PPS variations) and theGPS-PPS provides for longer term stability and wider area ‘coarse’synchronization. The transmitter system continuously monitors these twoPPS pulses (from the GPS unit and from the accurate clock source) andreports any anomaly. The anomalies could be that after the two PPSsources being in lock for several hours, one of the PPS sources driftsaway from the other source by a given time-threshold determined by thetower network administrator. A third local clock source can be used todetect anomalies. In case of anomalous behavior, the PPS signal whichexhibits the correct behavior is chosen by the transmitter system andreported back to the monitoring station. In addition, the instantaneoustime difference between the PPS input and PPS output of the accuratetime source (as reported by the time source) can either be broadcast bythe transmitter or can be sent to the server to be used when postprocessing.

In the transmitter system, the time difference between the rising edgeof the PPS pulse input and the rising edge of the signal that enablesthe analog sections of the transmitter to transmit the data is measuredusing an internally generated high speed clock. FIG. 14 shows a signaldiagram for counting the time difference between the PPS and the signalthat enables the analog sections of the transmitter to transmit thedata, under an embodiment. The count that signifies that difference issent to each of the receivers as a part of the data stream. Use of ahighly stable clock reference such as a Rubidium clock (the clock isstable over hours/days) allows the system to store/transmit thiscorrection per tower on the device, just in case the device cannotmodulate the specific tower data anymore. This correction data can alsobe sent via the communication medium to the device, if there is oneavailable. The correction data from the towers can be monitored byeither reference receivers or receivers mounted on the towers thatlisten to other tower broadcasts and can be conveyed to a centralizedserver. Towers can also periodically send this count information to acentralized server which can then disseminate this information to thedevices in the vicinity of those towers through a communication link tothe devices. Alternatively, the server can pass the information fromtowers (e.g., in a locale) to neighboring towers so that thisinformation can be broadcast as assistance information for theneighboring towers. The assistance information for neighboring towersmay include position (since the towers are static) and timing correctioninformation about towers in the vicinity.

Similar to the transmitter timing correction of an embodiment, when atrue PPS is available it can be used to estimate multipath bias andprecise true range. The receiver estimates range using samples of thesignal, for example from the ADC. The receiver of an embodiment uses ahigh speed clock to determine the difference between the occurrence ofthe PPS and the first edge of the sample ADC clock. This allows therange estimated by the receiver based on the ADC samples to be correctedfor the difference between when true PPS occurs and when the ADC samplesthe data, thus allowing for estimation of the true range of the receiverto a precision better than the sample clock resolution of the ADC. Inthe context of the discussion in the paragraph above, the PPS refers toa pulse whose edge is aligned to or has known offset from a standardtiming base such as GPS pulse-per-second (PPS) timing.

In another embodiment, a wide area differential positioning system canbe used to correct for timing errors from the towers. FIG. 15 is a blockdiagram of the differential WAPS system, under an embodiment. Areference receiver (located at a pre-surveyed location) is used toreceive signals from all the towers in the vicinity. Although theprinciples of differential GPS are applied in this method, dealing withthe effects of non-line-of-sight in the terrestrial case makes itunique. The reference receiver's pseudorange (code phase) measurementsfor each tower are time-tagged and then sent to the server. The receivedcode phase-based ranges measured at the reference receiver for towers jand i can be written as follows:

R _(ref) ^(j)(t)=ρ_(ref) ^(j) +c(dt _(ref) −dt ^(j))+ε_(R,ref) ^(j) ,R_(ref) ^(i)(t)=ρ_(ref) ^(i) +c(dt _(ref) −dt ^(i))+ε_(R,ref) ^(i),

where ρ_(ref) ^(j) is the reference receiver to transmit tower jgeometric range, dt_(ref) and dt^(j) are respectively the referencereceiver and transmitter clock offsets referred to their respectiveantennas with respect to a common reference time (say, GPS time), c isthe speed of light, and ε_(R,ref) ^(j) is the measurement noise.

The differences in clock timing between the towers i and j,dt^(i)−dt^(j) are computed at the server by subtracting the twoequations above and using the known geometric ranges from referencereceiver to the transmit towers. This allows for elimination of thetiming differences between the transmitters in the rover/mobile stationmeasurements. Note that averaging over time can be used to get better(e.g., less noisy) estimates of the time difference dt^(i)−dt^(j) whenthe clocks used in the transmit towers are relatively stable.

The rover/mobile station's pseudorange measurements are also time taggedand sent to a server. The received code phase based ranges measured atthe rover/mobile station can be written as:

R _(m) ^(i)(t)=ρ_(m) ^(i) +c(dt _(m) −dt ^(i))+ε_(R,m) ^(i) ,R _(m)^(j)(t)−ρ_(m) ^(j) +c(dt _(m) −dt ^(j))+ε_(R,m) ^(j).

By subtracting the two equations above and re-arranging, the result is

(ρ_(m) ^(j)−ρ_(m) ^(i))=(R _(m) ^(j)(t)−R _(m) ^(i)(t))−c(dt ^(i) −dt^(j))+(ε_(R,m) ^(i)−ε_(R,m) ^(j))

Note that R_(m) ^(j)(t) and R_(m) ^(i)(t) are measured quantities andthe quantity dt^(i)−dt^(j) is computed from the reference receivermeasurements. Each of ρ_(ref) ^(j) and ρ_(ref) ^(j) can be written interms of the unknown coordinates of the receiver and the knowncoordinates of the transmit towers i and j. With three rangemeasurements, two range difference equations can be formed as above toobtain a two-dimensional position solution or with four rangemeasurements, three range difference equations can be formed as above toobtain a three-dimensional position. With additional measurements, aleast square solution can be used to minimize the effect of the noisequantities ε_(R,m) ^(i) and ε_(R,m) ^(j).

Alternatively, the timing difference corrections can be sent back to themobile station to correct for the errors in-situ and to facilitateposition computation at the mobile station. The differential correctioncan be applied for as many transmitters as can be viewed by both thereference and the mobile stations. This method can conceptually allowthe system to operate without tower synchronization or alternatively tocorrect for any residual clock errors in a loosely synchronized system.

Another approach is a standalone timing approach as opposed to thedifferential approach above. One way of establishing timingsynchronization is by having GPS timing receivers at each Transmit towerin a specific area receive DGPS corrections from a DGPS referencereceiver in the same area. A DGPS reference receiver installed at aknown position considers its own clock as a reference clock and findscorrections to pseudo-range measurements to the GPS satellites ittracks. The DGPS correction for a particular GPS satellite typicallycomprises total error due to satellite position and clock errors andionospheric and tropospheric delays. This total error would be the samefor any pseudo-range measurement made by other GPS receivers in theneighborhood of the DGPS reference receiver (typically with an area ofabout 100 Km radius with the DGPS receiver at the center) because lineof sight between DGPS reference receiver and GPS satellite does notchange much in direction within this neighborhood. Thus, a GPS receiverusing DGPS correction transmitted by a DGPS reference receiver for aparticular GPS satellite uses the correction to remove this total errorfrom its pseudo-range measurement for that satellite. However in theprocess it would add the DGPS reference receiver's clock bias withrespect to GPS time to its pseudo-range measurement. But, since thisclock bias is common for all DGPS pseudo-range corrections, its effecton the timing solutions of different GPS receivers would be a commonbias. But this common bias gives no relative timing errors in thetimings of different GPS receivers. In particular, if these GPSreceivers are timing GPS receivers (at known positions) then all of themget synced to the clock of DGPS reference receiver. When these GPStiming receivers drive different transmitters, the transmissions alsoget synchronized.

Instead of using corrections from a DGPS reference receiver, similarcorrections transmitted by Wide Area Augmentation System (WAAS)satellites can be used by GPS timing receivers to synchronizetransmissions of the transmitters which they drive. An advantage of WAASis that the reference time is not that of the DGPS reference system butit is the GPS time itself as maintained by the set of accurate atomicclocks.

Another approach to achieving accurate time synchronization between thetowers across a wide area is to use time transfer techniques toestablish timing between pairs of towers. One technique that can beapplied is referred to as “common view time transfer”. FIG. 16 showscommon view time transfer, under an embodiment. The GPS receivers in thetransmitters that have the view of a common satellite are used for thispurpose. Code phase and/or carrier phase measurements from each of thetowers for the satellites that are in common view are time taggedperiodically (e.g., minimum of once every second) by the GPS receiversand sent to a server where these measurements are analyzed.

The GPS code observable R_(p) ^(i) (signal emitted by satellite “i” andobserved by a receiver “p”) can be written as: R_(p) ^(i)(t)=ρ_(p)^(i)+c(δ_(R) ^(i)+δ_(R,p)+T_(p) ^(i)+I_(p)^(i))+c(dt_(p)−dt^(i))+ε_(R,p),

where ρ_(p) ^(i), is the receiver-satellite geometric range equal to|{right arrow over (X)}_(p)−{right arrow over (X)}^(i)|, {right arrowover (X)}_(p) is the receiver antenna position at signal reception time,{right arrow over (X)}^(i) represents the satellite position at signalemission time, I_(p) ^(i) and T_(p) ^(i) are respectively theionospheric and tropospheric delays, and δ_(R) _(p) and δ_(R) ^(i) arethe receiver and satellite hardware group delays. The variable δ_(R)_(p) includes the effect of the delays within the antenna, the cableconnecting it to the receiver, and the receiver itself. Further, dt_(p)and dt^(i) are respectively the receiver and satellite clock offsetswith respect to GPS time, c is the speed of light, and ε_(R) is themeasurement noise.

The common view time transfer method computes the single difference codeobservable R_(pq) ^(i), which is the difference between code observablessimultaneously measured at two receivers (called “p” and “q”) as

$R_{pq}^{i} = {\underset{\underset{\underset{difference}{{geometrical}\mspace{14mu} {range}}}{}}{\rho_{p}^{i} - \rho_{q}^{i}} + \underset{\underset{\underset{{between}\mspace{14mu} {clocks}}{{time}\mspace{14mu} {difference}}}{}}{c\left( {{dt}_{p} - {dt}_{q}} \right)} + \underset{\underset{\underset{{delay}\mspace{14mu} {difference}}{{{Troposhpere}\mspace{11mu}\&}\mspace{11mu} {Ionosphere}}}{}}{{c\left( {T_{p}^{i} - T_{q}^{i}} \right)} + {c\left( {I_{p}^{i} - I_{q}^{i}} \right)}} + \underset{\underset{\underset{{between}\mspace{14mu} {receivers}}{{Group}\mspace{14mu} {delay}\mspace{14mu} {difference}}}{}}{c\left( {\delta_{R,p} - \delta_{R,q}} \right)} + \left( {ɛ_{R,p} - ɛ_{R,q}} \right)}$

calculating the single difference observable, the group delay in thesatellite as well as the clock error of the satellite gets cancelled.Also, note that in the above equation the tropospheric and ionosphericperturbations cancel (or, can be modeled, for example in cases where thereceiver separation is large). Once the group delay differences betweenthe receivers are calibrated, the desired time differencec(dt_(p)−dt_(q)) between the receiver clocks can be found from theequation. The single difference across multiple time and satellitemeasurements can be combined to further improve the quality of theestimated time difference.

In a similar manner, the single difference carrier phase equation forcommon view time transfer can be written as:

$\Phi_{pq}^{i} = {\underset{\underset{\underset{difference}{{geometrical}\mspace{14mu} {range}}}{}}{\rho_{p}^{i} - \rho_{q}^{i}} + \underset{\underset{\underset{{between}\mspace{14mu} {clocks}}{{time}\mspace{14mu} {difference}}}{}}{c\left( {{dt}_{p} - {dt}_{q}} \right)} + \underset{\underset{\underset{{delay}\mspace{14mu} {difference}}{{{Troposhpere}\mspace{11mu}\&}\mspace{11mu} {Ionosphere}}}{}}{{c\left( {T_{p}^{i} - T_{q}^{i}} \right)} + {c\left( {I_{p}^{i} - I_{q}^{i}} \right)}} + \underset{\underset{\underset{{between}\mspace{14mu} {receivers}}{{Group}\mspace{14mu} {delay}\mspace{14mu} {difference}}}{}}{c\left( {\delta_{\varphi,p} - \delta_{\varphi,q}} \right)} + \underset{\underset{\underset{phase}{{initial}\mspace{14mu} {ambiguity}\mspace{14mu} i\; n}}{}}{\lambda \left( {\varphi_{p}^{i} - \varphi_{q}^{i}} \right)} + \underset{\underset{{phase}\mspace{14mu} {measurement}}{{integer}\mspace{14mu} {ambiguity}\mspace{14mu} i\; n}}{\underset{}{\lambda \left( {N_{p}^{i} - N_{q}^{i}} \right)}} + {\left( {ɛ_{\varphi,p} - ɛ_{\varphi,q}} \right).}}$

Note that since initial phase ambiguity and integer ambiguity arepresent in the above equation, the phase single difference cannot beused to determine the time transfer directly. A combined use of the codeand phase observations allows for advantage to be taken of the absoluteinformation about time difference from the codes and the preciseinformation about the evolution of time difference from the carrierphases. The error variance in the carrier phase single difference issignificantly better than the code phase single difference leading tobetter time transfer tracking.

The resulting errors per tower for a given satellite are either sentback to the tower for correction, applied at the tower, sent to thereceivers over the communication link for the additional corrections tobe done by the receiver, or sent as a broadcast message along with othertiming corrections from the tower. In specific instances, it might besuch that the measurements from the towers and the receiver arepost-processed on the server for better location accuracy. A singlechannel GPS timing receiver or a multiple channel timing receiver thatproduces C/A code measurements and/or carrier phase measurements from L1and/or L2 or from other satellite systems such as Galileo/Glonass can beused for this purpose of common view time transfer. In multiple channelsystems, information from multiple satellites in common view arecaptured at the same instant by the receivers.

An alternative mechanism in “common view time transfer” is to ensurethat different timing GPS receivers in the local area (each feeding toits corresponding transmitter) use only common satellites in theirtiming pulse derivation (e.g., one pulse per second) but no attempt ismade to correct the timing pulses to be aligned to the GPS (or UTC)second. The use of common view satellites ensure that common errors intiming pulses (such as common GPS satellite position and clock errorsand ionospheric and tropospheric delay compensation errors) pull theerrors in timing pulse by about same magnitude and relative errors intiming pulses are reduced. Since, in positioning, only relative timingerrors matter, there is no need for any server-based timing errorcorrection. However, a server can give commands to different GPSreceivers on which GPS satellites are to be used in deriving timingpulses.

An alternative method of time transfer is the “two-way time transfer”technique. FIG. 17 shows the two-way time transfer, under an embodiment.Consider two towers that are used to time against each other.Transmissions from each of the two transmitters starts on the PPS pulseand a time interval counter is started on the receive section (WAPSReceiver) of the transmit towers. The received signal is used to stopthe time interval counter on either side. The results from the timeinterval counter are sent over the data modem link to the WAPS serverwhere these results along with transmit times are compared and theerrors in timing between the two towers can be computed. This can thenbe extended to any number of towers. In this method, the relationshipbetween the counter measurements ΔT_(i) at tower i and ΔT_(j) at towerj, and the time difference dt_(ij) between the clock in i and j can berepresented as

dt _(ij) =T _(i) −T _(j)=½(ΔT _(i) −ΔT _(j))+½[(τ_(i) ^(Tx)+τ_(j)^(Rx))−(τ_(j) ^(Tx)+τ_(i) ^(Rx))],

where τ_(i) ^(Tx) & τ_(j) ^(Tx) are the transmitter delays of thetowers, and τ_(i) ^(Rx) & τ_(j) ^(Rx) are the receiver delays of towers.The time difference can be estimated once the transmitter and receiverdelays are calibrated.

In addition to the time transfer between towers, the timing of thetowers relative to GPS time can be found by the GPS timing receiversused in common view time transfer. Using the range measurement as

R _(p) ^(i)(t)=ρ_(p) ^(i) +c(δ_(R) ^(i)+δ_(R,p) +T _(p) ^(i) +I _(p)^(i))+c(dt _(p) −dt ^(i))+ε_(R,p),

the time correction of local clock relative to GPS time dt_(p) iscomputed, after accounting for the delay of the receiver, satelliteclock errors and ionospheric/tropospheric errors. The delay of thereceiver δ_(R,p) can be calibrated by measurement of the group delay.Information from the GPS satellite navigation message (either obtainedthrough demodulation or from a server) can be used to compute thesatellite timing correction which eliminates the effect of dt^(i) andδ_(R) ^(i). Similarly, troposphere and ionosphere delay effects areminimized using the corrections from an external model. Ionosphericcorrections can be obtained for example from WAAS messages.Alternatively, a combination of clock and ionospheric/troposphericcorrections can be obtained from RTCM DGPS corrections for thepseudorange, when available.

The offset relative to GPS time can also be sent as part of the datastream from the towers. This enables any WAPS receiver that acquires theWAPS signal to provide accurate GPS time and frequency aiding tosignificantly reduce GNSS search requirements in a GNSS receiver.

In an embodiment of the system, the broadcast transmitters can beemployed ad hoc to provide localized indoor position determination. Forexample, in a fire-safety application, the WAPS transmitters would beplaced on three or more broadcast stations (could be fire trucks, forexample). The towers would synchronize to each other by one of the manymeans described earlier and broadcast signals. The bandwidth andchipping rates would be scaled based on spectrum availability andaccuracy requirements in that area for that application at that time.The receivers would be notified of the system parameters through thecommunication link to the devices.

FIG. 18 is a block diagram of a receiver unit, under an embodiment. Thebeacon signal is received at the antenna on the receiver unit,down-converted, demodulated and decrypted and fed to the positioningengine. The receiver provides all information to reconstruct the signalaccurately. The receive antenna can be an omni-directional antenna or,alternatively, a number of antennas/arrays providing diversity etc. Inanother embodiment, the mixing and down conversion can be done in thedigital domain. Each receiver unit includes or uses a unique hardwareidentification number and a computer generated private key. Eachreceiver unit, in general, stores the last few locations in non volatilememory and can be later queried remotely for the last few storedlocations. Based on the availability of the spectrum in a given area,the transmitters and receivers can adapt to the available bandwidth andchange the chipping rate and filter bandwidths for better accuracy andmultipath resolution.

In one embodiment, the digital baseband processing of the receivedsignals is accomplished using commercially-available GPS receivers bymultiplexing/feeding the signal from a GPS RF section with the WAPS RFmodule. FIG. 19 is a block diagram of the receiver with a WAPS RFmodule, under an embodiment. The RF module includes one or more of Lownoise amplifiers (LNAs), filters, down-converter, and analog to digitalconverters, to name a few. In addition to these components, the signalcan be further conditioned to fit the input requirements of the GPSreceiver using additional processing on chip or a custom ASIC or on anFPGA or on a DSP or on a microprocessor. The signal conditioning caninclude digital filtering for in-band or out-of band noise (such asACI—adjacent channel interference), translating intermediate or basebandfrequencies of the input to the GPS IC from the frequencies of the WAPSreceiver, adjusting the digital signal strength so that the GPS IC willbe able to process the WAPS signal, automatic gain control (AGC)algorithms to control the WAPS frontend etc. In particular, thefrequency translation is a very useful feature because this allows theWAPS RF module to work with any commercially available GPS receiver. Inanother embodiment, the entire RF frontend chain including the signalconditioning circuits for the WAPS system can be integrated onto anexisting GPS die that contains a GPS RF chain.

In another embodiment, if access to the digital baseband input is notavailable, the signal can be up-converted/down-converted from any bandto the GPS band and fed into the RF section of the GPS receiver. FIG. 20shows signal up-conversion and/or down-conversion, under an embodiment.

In another embodiment, multiple RF chains or tunable RF chains can beadded to both the transmitter and receiver of the WAPS system so as touse the most effective frequency of operation in a given area, be itwide or local. The choice of frequency can be determined by cleanlinessof the spectrum, propagation requirements, etc.

Similarly, WAPS can temporarily use a receive chain in a receiver systemthat includes multiple receive chains. For example, a wideband CDMA(W-CDMA) receiver system includes two receive chains to improve receivediversity. Thus, when WAPS is used in a W-CDMA receiver system one ofthe two native receive chains of the W-CDMA can be used temporarily forreceiving and processing WAPS signals. FIG. 21 is a block diagram of areceiver system having multiple receive chains in which one of thereceive chains can be used temporarily for receiving and processing WAPSsignals, under an embodiment. In this example, the diversity receivechain can be used to temporarily receive and process the WAPS signals.Alternatively, the GPS receive chain can be used to temporarily receiveand process the WAPS signals.

The radio front-end can be shared between WAPS and another application.Some parts of the frontend can be shared and some may be used on amutually exclusive basis. For example, if the die/system already has aTV (NTSC or ATSC or systems like DVB-H, MediaFLO) tuner front-endincluding the antenna, the TV tuner radio and antenna can be shared withthe WAPS system. They can operate on a mutually exclusive basis in that,either the system receives TV signals or receives WAPS signals at anygiven time. In another embodiment, if it makes it easier to add a WAPSRF section to such a system, the antenna can be shared between the TVtuner and the WAPS system allowing both systems to operatesimultaneously. In cases where the system/die has a radio like an FMradio, the RF front-end can be modified to accommodate both the WAPSsystem and the FM radio and these radios can operate on a mutuallyexclusive basis. Similar modifications can be done for systems that havesome RF frontends that operate in close frequency proximity to the WAPSRF band.

The clock source reference such as crystal, crystal oscillator (XO),Voltage Controlled Temperature Compensated Crystal Oscillator (VCTCXO),Digitally-controlled Crystal Oscillator (DCXO), Temperature CompensatedCrystal Oscillator (TCXO), that is used for a GNSS sub-system can beshared with the WAPS receiver to provide the reference clock to the WAPSreceiver. This sharing can be done on the die or off-chip.Alternatively, the TCXO/VCTCXO used by any other system on a cellularphone can shared with the WAPS system. FIG. 22 is a block diagramshowing clock sharing in a positioning system, under an embodiment. Notethat the transceiver or processor system block can refer to a variety ofsystems. The transceiver system that shares the clock with the WAPSsystem can be a modem transceiver (for example, a cellular or WLAN or BTmodem) or a receiver (for example, a GNSS, FM or DTV receiver). Thesetransceiver systems may optionally control the VCTCXO or DCXO forfrequency control. Note that the transceiver system and the WAPS systemmay be integrated into a single die or may be separate dies and does notimpact the clock sharing. The processor can be any CPU system (such asan ARM sub-system, Digital Signal Processor system) that uses a clocksource. In general, when a VCTCXO/DCXO is shared, the frequencycorrection applied by the other system may be slowed down as much aspossible to facilitate WAPS operation. Specifically, the frequencyupdates within the maximum integration times being used in WAPS receivermay be limited to permit better performance (i.e. minimizing SNR loss)for the WAPS receiver. Information regarding the state of the WAPSreceiver (specifically, the level of integration being used, acquisitionversus tracking state of the WAPS system) can be exchanged with theother system for better coordination of the frequency updates. Forexample, frequency updates could be suspended during WAPS acquisitionphase or frequency updates can be scheduled when the WAPS receiver is insleep state. The communication could be in the form of control signalsor alternatively in the form of messages exchanged between thetransceiver system and the WAPS system.

The WAPS broadcasts signals and messages from the towers in such a waythat a conventional GPS receiver's baseband hardware need not bemodified to support both a WAPS and a traditional GPS system. Thesignificance of this lies in the fact that although the WAPS system hasonly half the available bandwidth as the GPS C/A code system (whichaffects the chip rate), the WAPS broadcast signal is configured tooperate within the bounds of a commercial grade C/A code GPS receiver.Further, based on signal availability, the algorithms will decidewhether GPS signals should be used to determine position or WAPS signalsor a combination thereof should be used to get the most accuratelocation.

The data transmitted on top of the gold codes on the WAPS system can beused to send assistance information for GNSS in the cases of a hybridGNSS-WAPS usage scenario. The assistance can be in the form of SV orbitparameters (for example, ephemeris and almanac). The assistance may alsobe specialized to SVs visible in the local area.

In addition, the timing information obtained from the WAPS system can beused as fine time aiding for the GNSS system. Since the WAPS systemtiming is aligned to GPS (or GNSS) time, aligning to the code and bit ofWAPS signal and reading the data stream from any tower provides coarseknowledge of GNSS time. In addition, the position solution (thereceiver's clock bias is a by-product of the position solution)determines the WAPS system time accurately. Once the WAPS system time isknown, fine time aiding can be provided to the GNSS receiver. The timinginformation can be transferred using a single hardware signal pulsewhose edge is tied to the internal time base of WAPS. Note that the WAPSsystem time is directly mapped onto GPS time (more generally, with GNSStime, since the time bases of GNSS systems are directly related). TheGNSS should be able to latch its internal GNSS time base count uponreceipt of this edge. Alternatively, the GNSS system should be able togenerate a pulse whose edge is aligned to its internal time base and theWAPS system should be capable of latching its internal WAPS time base.The WAPS receiver then sends a message with this information to the GNSSreceiver allowing the GNSS receiver to map its time base to WAPS timebase.

Similarly, the frequency estimate for the local clock can be used toprovide frequency aiding to the GNSS receiver. Note that frequencyestimate from WAPS receiver can be used to refine the frequency estimateof the GNSS receiver whether or not they share a common clock. When thetwo receivers have a separate clock, an additional calibration hardwareor software block is required to measure the clock frequency of onesystem against the other. The hardware or software block can be in theWAPS Receiver section or in the GNSS receiver section. Then, thefrequency estimate from the WAPS receiver can be used to refine thefrequency estimate of the GNSS receiver.

The information that can be sent from the WAPS system to the GNSS systemcan also include an estimate of location. The estimate of location maybe approximate (for example, determined by the PN code of the WAPStower) or more accurate based on an actual position estimate in the WAPSsystem. Note that the location estimate available from the WAPS systemmay be combined with another estimate of position from a differentsystem (for example, a coarse position estimate from cellular ID basedpositioning) to provide a more accurate estimate of position that can beused to better aid the GNSS system. FIG. 23 is a block diagram ofassistance transfer from WAPS to GNSS receiver, under an embodiment.

The GNSS receiver can also help improve the performance of the WAPSreceiver in terms of Time-To-First-Fix (TTFF), sensitivity and locationquality by providing location, frequency and GNSS time estimates to theWAPS receiver. As an example, FIG. 24 is a block diagram showingtransfer of aiding information from the GNSS receiver to the WAPSreceiver, under an embodiment. Note that the GNSS system can be replacedby LORAN, e-LORAN or similar terrestrial positioning system as well. Thelocation estimate can be partial (eg. Altitude or 2-D position), orcomplete (eg. 3-D position) or raw range/pseudo-range data). Therange/pseudo-range data should be provided along with the location of SV(or means to compute the location of the SV such as SV orbit parameters)to enable usage of this range information in a hybrid solution. Alllocation aiding information should be provided along with a metricindicating its quality. When providing GNSS time information (which maybe transferred to the WAPS system using a hardware signal), the offsetof GNSS time relative to GPS time (if any) should be provided to enableusage in the WAPS receiver. Frequency estimates, can be provided as anestimate of the clock frequency along with a confidence metric(indicating the estimated quality of the estimate, for example, themaximum expected error in the estimate). This is sufficient when theGNSS and WAPS systems share the same clock source. When the GNSS andWAPS systems use a separate clock, the GNSS clock should also beprovided to the WAPS system to enable the WAPS system to calibrate (i.e.estimate the relative clock bias of WAPS with respect to GNSS clock) or,alternatively, the WAPS system should provide its clock to the GNSSsystem and the GNSS system should provide a calibration estimate (i.e.an estimate the relative clock bias of WAPS with respect to GNSS clock).

To further improve the sensitivity and TTFF of a WAPS receiver,assistance information (such as that would otherwise be decoded from theinformation transmitted by the towers) can be provided to the WAPSreceiver from a WAPS server by other communication media (such ascellular phone, WiFi, SMS etc). With the “almanac” information alreadyavailable, the WAPS receiver's job becomes simple since the receiverjust needs to time align to the transmit waveform (without requirementof bit alignment or decoding). The elimination of the need to decode thedata bits reduces TTFF and therefore saves power since the receiver doesnot need to be continuously powered on to decode all the bits. FIG. 25is an example configuration in which WAPS assistance information isprovided from a WAPS server, under an embodiment.

A beacon may be added to the receiver to further improve localpositioning. The beacon can include a low power RF transmitter thatperiodically transmits a waveform with a signature based on a device ID.For example, the signature can be a code that uniquely identifies thetransmitter. An associated receiver would be able to find a location ofthe transmitter with a relatively higher accuracy through either signalenergy peak finding as it scans in all directions, or through directionfinding (using signals from multiple-antenna elements to determinedirection of signal arrival).

Resolution of Multipath Signals

Resolution of multipath is critical in positioning systems. Wirelesschannel is often characterized by a set of randomly varying multipathcomponents with random phases and amplitudes. For positioning to beaccurate, it is imperative that the receiver algorithm resolves theline-of-sight (LOS) path if present (it will be the first arriving path)or the path that arrives first (which may not necessarily be the LOScomponent).

Traditional methods often work as follows: (1) the received signal iscross-correlated with the transmitted pseudo-random sequence (e.g. Goldcode sequence, which is known at the receiver); (2) the receiver locatesthe first peak of the resulting cross-correlation function and estimatesthat the timing of the path that arrived first is the same as the timingindicated by the position of this peak. These methods work effectivelyas long as the lowest multipath separation is much larger than inverseof the bandwidth available which is often not the case. Bandwidth is aprecious commodity and a method which can resolve multipath with theminimal amount of bandwidth is highly desired to improve the efficiencyof the system.

Depending on the channel environment (including multipath and signalstrength), an appropriate method for obtaining an estimate of theearliest arriving path is used. For best resolvability, high-resolutionmethods are used whereas for reasonable performance at low SNRs moretraditional methods that directly use the cross-correlation peak samplesand some properties of the correlation function around the peak areapplied.

Consider the quantized received signal y[n] sampled at a rate f_(s)given by:

y[n]=h_(eff)[n]⊗x[n], y[n]=Σ_(i=n) ₀ ^(∞) h_(eff)[i]·x[n−i], where y[n]is the received signal which is the convolution of the transmittedpseudo-random sequence x[n] with the effective channelh_(eff)[n]=h[n]⊗h_(tx)[n]⊗h_(rx)[n], where h_(tx)[n] is the transmitfilter, h_(tx)[n] is the receive filter and h[n] is the multi-pathchannel.

One method to find the peak position is by peak interpolation using thevalues surrounding the apparent peak position. The interpolation may bequadratic using one value on either side of the peak or may use a higherorder polynomial using two or more samples around the peak or may use abest fit for the actual pulse shape. In the case of quadraticinterpolation, a quadratic is fitted to the peak value and the valuesimmediately surrounding the peak. The peak of the quadratic determinesthe peak position that is used for ranging. This method is quite robustand can work well at low SNR. An alternative embodiment may use a valueother than the peak position as the reference position. Note that theDLL actually uses the peak position as reference position on thecorrelation function whereas this method uses a point different from thepeak as reference. This method is motivated by the fact that the earlyedge of the correlation peak is less affected by multi-path than thetrailing edge. For example, a point 75% of chip T_(c) from the peak onthe undistorted (without channel effects) correlation function may beused as a reference point. In this case, the portion of the interpolatedz[n] function that matches this 75% point is selected and the peak isfound as 25% of T_(c) away from this point. Another alternative peakcorrelation function based method may use the peak shape (such as ameasure of distortion of the peak, for example, peak width). Startingfrom the peak location and based on the shape of the peak, a correctionto the peak location is determined to estimate the earliest arrivingpath.

High-resolution methods are a class of efficient multipath-resolutionmethods which use Eigen-space decompositions to locate the multipathcomponents. Methods such as MUSIC, ESPIRIT fall under this class ofresolution schemes. They are highly powerful schemes as in they canresolve effectively much more closely spaced multipath components thantraditional methods, for the same given bandwidth. The high resolutionearliest time of arrival method attempts to estimate directly the timeof arrival of earliest path rather than inferring the peak position fromthe peak values. The below assumes that a coarse-acquisition of thetransmitted signal is already available at the receiver and the start ofthe pseudo-random sequence is known roughly at the receiver.

FIG. 26 is a flow diagram for estimating an earliest arriving path inh[n], under an embodiment. The method to determine the earliest pathcomprises the following operations, but is not so limited:

-   -   1. Cross-correlate the received samples y[n] with the transmit        sequence x[n] to obtain the result z[n]. When the        cross-correlation is written in terms of a convolution,

z[n]=y[n]⊗x*[−n]

-   -    The equation can be re-written as

z[n]=h _(eff)[n]⊗ϕ_(xx)[n]

-   -    where ϕ_(xx)[n] is the autocorrelation function of the        pseudo-random sequence    -   2. Locate the first peak of z[n] and denote it as n_(peak).        Extract wL samples to the left of the peak and wR samples to the        right of the peak of z[n] and denote this vector as pV.

pV=[z[n _(peak) −wL+1] . . . Z[n _(peak) +wR]]

-   -    The vector pV denotes the useful part of the cross-correlation        result z[n]. In the ideal case, in the absence of channel        distortion and when the channel BW is not limited, the choosing        wL=wR=ƒ_(s)T_(c) would be sufficient to determine the timing of        the received signal. In the presence of limited BW, for the case        when the pseudo-random code x[n] is a sequence of +1/−1's, the        optimal method to choose wL and wR are to choose them as the        non-zero values (or, more generally, values >a certain threshold        defined as a fraction of the peak value are selected) present on        the left and right side of the peak of p[n]=h_(tx)[n]⊗h_(tx)[n]        respectively. One other consideration in the choice of wL and wR        is to select enough uncorrelated noise samples to obtain enough        information regarding the noise sub-space. In addition, the        integers wL and wR should be chosen to include all possible        multipath components especially on the left side (i.e. through        choice of wL) to help resolve far-out multipath components.        Including too many samples beyond ƒ₅T_(c) increases the amount        of noise introduced in the pV vector and hence has to be        curtailed. Through simulation and experiments, a typical set of        values for wL and wR are 3ƒ_(s)T_(c) and 3ƒ_(s)T_(c),        respectively. Note that z[n] (and in turn pV) contains the        effect of the channel h[n], the transmit filter h_(tx)[n], the        receive filter h_(rx)[n] and the autocorrelation function of the        pseudo-random sequence ϕ_(xx)[n]. In order to estimate the        earliest arriving path in the channel, the other effects need to        be eliminated. In many cases the transmit and receive        pulse-shapes are matched for best noise performance, but that        constraint is not required for this algorithm to work. The        reference correlation function is defined as        ϕ_(ref)[n]=ϕ_(xx)[n]⊗h_(tx)[n]⊗h_(rx)[n] which needs to be        estimated and eliminated before pV can be used for estimation of        earliest arriving path.    -   3. The Reference correlation function ϕ_(ref)[n] is estimated        next.        -   One method to obtain the reference cross-correlation is as            follows: perform steps 1-2 on a ideal channel (a so called            “cabled link”) to obtain the corresponding peak vector            pV_(Ref). The peak vector pV_(Ref) contains the useful            samples of the reference correlation function ϕ_(ref)[n].            FIG. 27 is a flow diagram for estimating reference            correlation function, under an embodiment.        -   The “Cabled link” method involves sending the modulated            signal from the transmitter front-end (power-amplifier and            transmit antenna is by-passed) through an ‘ideal’ channel            (for example, a cable) to the receiver front-end (bypass the            receive antenna). Note that the ‘ideal’ channel can have            some delay and attenuation, but should not add any other            distortion and must have high SNR. For the best performance,            the ‘cabled’ reference needs to be generated separately for            each pseudo-random sequence as they have different            autocorrelation functions and hence different references. It            is also then critical to choose PRNs properly for the best            autocorrelation functions (specifically, their close in            autocorrelation side-lobes should be well suppressed            compared to the peak) which will result in the best overall            performance of the timing-resolution method, since            autocorrelation sidelobes can get mistaken for multipath            unless sufficiently attenuated        -   Assuming transmit filter responses are controlled, one            calibration of the response on cabled link is required per            receiver during production. If receiver filter            characteristics can be controlled (for example, for a bunch            of receivers), then the calibration on cabled link of the            response can be further reduced to one calibration            measurement for a set of receivers. An alternative method            for determining the reference correlation function            ϕ_(ref)[n] is to compute the individual components            ϕ_(xx)[n], h_(tx)[n] and h_(rx)[n] analytically and to            convolve them to arrive at the reference correlation            function ϕ_(ref)[n]. Note that this method depends on the            extent to which transmit and receive filter impulse            responses can be controlled in an actual implementation.    -   4. Improve the SNR in the estimate of pV by coherently averaging        across multiple gold codes and even across multiple bits.        Averaging across multiple bits can be done coherently after        decisions on the individual bits being transmitted have been        made. In other words using decision feedback before integration        across bits. Note that improved SNR can be obtained equivalently        by performing averaging in the cross-correlation function        estimation in Step1.    -   5. Calculate the Fast Fourier Transform (FFT) of length N_(fft)        of pV and pV_(Ref) with zero padding of N_(fft)−(wL+wR) zeros to        obtain the length N_(fft) vectors pV_(Freq) and pV_(Ref,Freq)        respectively. An optimal value for Nif is obtained by checking        resolvability of multipath through simulations using both        synthetic and real measured channels. A typical value of Nif was        found to be greater than or equal to 4096. The

pV _(Freq)=FFT[pV zeropad],pV _(Ref,Freq)=FFT[pV _(Ref) zeropad]

-   -   6. Calculate

${H_{full}\lbrack k\rbrack} = \frac{{pV}_{Freq}\lbrack k\rbrack}{{pV}_{{Ref},{Freq}}\lbrack k\rbrack}$

-   -    to obtain the frequency domain estimate (corrupted with noise)        of the channel h[n]. If the received sequence y [n] is        oversampled by N_(os)

$\left( {{i.e.\mspace{14mu} N_{os}} = {{\frac{f_{s}T_{c}}{2}\mspace{14mu} {for}\mspace{14mu} a\mspace{14mu} {transmit}\mspace{14mu} {pulse}\mspace{14mu} {shape}\mspace{14mu} {band}\text{-}{limited}\mspace{14mu} {to}}\mspace{14mu} + {{/{- 1}}/{Tc}}}} \right)$

-   -    and if the transmit and receive pulse-shaping filters are        perfectly band-limited with BW=1/Tc, then exactly

$N = \frac{N_{fft}}{2N_{os}}$

-   -    positive and negative samples around DC of H_(full)[k] are        non-zero (i.e. usable) for estimation of the real channel,        H_(real)[k]. From our studies, we have concluded that

$\frac{N_{fft}}{2\alpha \; N_{os}}$

-   -    samples on either side of DC should be picked for the best        performance of the resolution algorithm, where α>1 is chosen        based on the actual pulse-shaping filters used at the        transmitter and receiver and the autocorrelation function        ϕ_(xx)[n]. Note that including the frequency transition band of        ϕ_(ref)[n] causes noise enhancement and α is chosen large enough        to exclude these frequencies in the selected samples. However,        choosing α too large will cause loss of signal information. A        preferred choice of α=1.25 for real band-limited functions based        on raised-cosine filter shapes with small excess bandwidth has        been used in the implementation.    -   7. If the DC component of H_(full)[k] is at index 0, the reduced        H vector, H[ ] is defined as:

H=[H _(full)[N _(fft) −N+1] . . . H _(full)[N _(fft)]H _(full)[0]H_(full)[1] . . . H _(full)[N]]

-   -   8. Construct the matrix P from the reduced channel estimate        vector H[k],

$P = \begin{bmatrix}{H(M)} & \cdots & {H\left( {{2N} - 1} \right)} & {H^{\prime}(0)} & \cdots & {H^{\prime}\left( {{2N} - M + 1} \right)} \\{H\left( {M - 1} \right)} & \cdots & {H\left( {{2N} - 2} \right)} & {H^{\prime}(1)} & \cdots & {H^{\prime}\left( {{2N} - M + 2} \right)} \\\vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\{H(0)} & \cdots & {H\left( {{2N} - M + 1} \right)} & {H^{\prime}(M)} & \cdots & {H^{\prime}\left( {{2N} - 1} \right)}\end{bmatrix}$

-   -    where 1<M<2N is a parameter and ( )′ represents conjugate of        the complex number. Define the estimated covariance matrix R of        the reduced channel estimate vector H[k] as

R=P×P′

-   -    If M is chosen to be too small (close to 1), then the        eigen-values of R are very limited in number and, as a result,        the high-resolution algorithm cannot delineate between the        signal and noise. If M is chosen too large (close to 2N), then        the covariance matrix estimate R is unreliable as the amount of        averaging in obtaining the covariance is inadequate and also the        covariance matrix R obtained is rank-deficient. Thus, a value of        M which is right in the middle of its allowable range i.e. M=N        is a good choice. This has also been verified empirically.    -   9. Perform singular value decomposition (SVD) on R as R=UDV′        where U is a matrix of the left singular vectors, V is the        matrix of the right singular vectors and D is the diagonal        matrix of singular values.    -   10. Construct the vector of sorted singular values sV as        -   sV=diagonal elements of D sorted in descending order    -   11. The next key step is to separate the signal and noise        subspaces. In other words, to select an index ns in the vector        sV such that the singular values sV[ns+1] . . . sV[N] correspond        to noise. Define a vector of noise singular values as        sV_(noise).        -   There are a number of methods possible to separate the            singular values corresponding to the noise subspace and find            a representation for the basis vectors of the noise            sup-space:        -   a) All singular values which are smaller than

$\frac{\max ({sV})}{T_{1}}$

-   -   -    where T₁ is a threshold value which is a function of the            signal-noise ratio (e.g. SNR on the chip) T₁=ƒ(SNR).            -   FIG. 28 is a flow diagram for estimating noise                sub-space, under an embodiment.        -   b) All singular values less than min

$\left( {\frac{\max ({sV})}{T_{1}},{{{mean}\left( {{sV}\left( {L:M} \right)} \right)} \times T_{2}}} \right),$

-   -   -    where L is a parameter which can be chosen greater than            delay-spread (e.g. N/2) and T₂ is another threshold value            determined empirically (typical value can be 1000).            -   FIG. 29 is a flow diagram for estimating noise                sub-space, under an alternative embodiment.        -   c) Another method involves determining the noise subspace by            repeatedly estimating the SNR for different partitions of            noise and signal-plus-noise subspaces and comparing with            another estimate of SNR. FIG. 30 is a flow diagram for            estimating noise sub-space, under another alternative            embodiment.            -   1) Calculate estimate of SNR as follows:                -   i. Assume that the noise is represented by the sV( )                    n_(s),n_(s)+1 . . . M, Calculate noise variance as:

${\sigma_{est}^{2}\left( n_{s} \right)} = \frac{\sum_{i = n_{s}}^{M}{{sV}(i)}}{M - n_{s} + 1}$

-   -   -   -   -   ii. Calculate the signal power as                    P_(sig)(n_(s))=Σ_(i=1) ^(n) ^(s) ⁻¹(sV(i)−σ_(est)                    ²(n_(s)))                -   iii. Estimate of SNR:

${{SNR}_{est}\left( n_{s} \right)} = \frac{P_{sig}\left( n_{s} \right)}{\sigma_{est}^{2}\left( n_{s} \right)}$

-   -   -   -   2) An alternative estimate of SNR is obtained through                other methods (e.g. SNR on chip). One method of                estimating SNR directly is as follows:                -   i. If the received data samples (after frequency                    error removal and re-sampling to Tc-spaced samples                    and code de-correlation) are given by X_(i)(where                    the X_(i) are chip-spaced starting from the                    interpolated peak position).

X _(i) =S+N _(i)

-   -   -   -   -   ii. The signal is estimated as

$\hat{S} = {\frac{1}{N}{\sum_{i = 0}^{N - 1}X_{i}}}$

-   -   -   -   -   iii. The noise is estimated as

$\hat{N} = {\frac{1}{N - 1}{\sum_{i = 0}^{N - 1}\left( {X_{i} - \hat{S}} \right)^{2}}}$

-   -   -   -   -   iv. The SNR is estimated as

$= \frac{\hat{S}}{\hat{N}}$

-   -   -   -   3) Choose the noise singular values as sV(ns, ns+1, . .                . ,M) which satisfy the following condition:

n _(start)=[smallest n _(s):SNR_(est)(n _(s))>

]

-   -   -   d) Another method involves determining the noise subspace by            repeatedly estimating the SNR for different partitions of            noise and signal subspaces using c)1) and choosing a            partition n_(start) such that n_(start)=argmax _(n) _(s)            [SNR_(est) (n_(s))−SNR_(est) (n_(s) −1)]_(n) _(s) ₌₂ ^(K).            -   FIG. 31 is a flow diagram for estimating noise                sub-space, under yet another alternative embodiment.        -   e) FIG. 32 is a flow diagram for estimating noise sub-space,            under still another alternative embodiment.            -   1) Define

${wLen} = {\frac{{wL} + {wR}}{f_{s}T_{c}}.}$

-   -   -   -    Then the first wLen singular values represent the                significant signal-plus-noise subspace or noise subspace                singular values (the rest of the singular values                represent correlated noise and signal and quantization                effects).            -   2) Calculate estimate of SNR as follows:                -   i. Assume that the noise is represented by the                    sV(i):i=n_(s), n_(s)+1 . . . wLen; 1<n_(s)≤wLen,                    calculate noise variance as:

${\sigma_{est}^{2}\left( n_{s} \right)} = \frac{\sum_{i = n_{s}}^{wLen}{{sV}(i)}}{{wLen} - n_{s} + 1}$

-   -   -   -   -   ii. Calculate the signal power as                    P_(sig)(n_(s))=Σ_(i=1) ^(n) ^(s) ⁻¹[sV(i)−σ_(est)                    ²(n_(s))]                -   iii. Estimate of SNR:

${{SNR}_{est}\left( n_{s} \right)} = \frac{P_{sig}\left( n_{s} \right)}{\sigma_{est}^{2}\left( n_{s} \right)}$

-   -   -   -   3) Define n_(start)=[smallest n_(s):                SNR_(est)(n_(s))>(SNR_(est)(wLen)−thresDB)]. Then                n_(start) up to winLen represent the noise singular                values. A typical value of thresDB is 10.

    -   12. Choose the corresponding noise right-singular vectors to        build V_(N) i.e. choose all vectors in V which correspond to the        noise singular values and build the noise subspace matrix V_(N).

    -   13. Estimate Time of Arrival of the first path:

${\left. {{{\left. a \right)\mspace{14mu} {Define}\mspace{14mu} {\omega (\tau)}} = \begin{bmatrix}1 & e^{\frac{j\; 2\pi}{N_{fft}}\tau} & e^{\frac{j\; 2\pi}{N_{fft}}2\tau} & e^{\frac{j\; 2\; \pi}{N_{fft}}3\tau} & \cdots & e^{\frac{j\; 2\; \pi}{N_{fft}}{({M - 1})}\tau}\end{bmatrix}^{H}}b} \right)\mspace{14mu} {Calculate}\mspace{14mu} {\Omega (\tau)}} = {\frac{1}{{\omega (\tau)}^{H}V_{N}V_{N}^{H}{\omega (\tau)}}\mspace{14mu} {for}\mspace{14mu} a\mspace{14mu} {range}\mspace{14mu} {of}\mspace{14mu} {values}\mspace{14mu} {of}\mspace{14mu} {{\tau \left( {\tau \in \left\lbrack {\tau_{m\; {ax}},{- \tau_{m\; {ax}}}} \right\rbrack} \right)}.}}$

-   -    The resolution of search Δτ can be chosen as small as required.        As an example, τ_(max)=5 and Δτ=0.05 so that z is searched for        in the range [−5,5] in steps of 0.05.    -   14. Peaks of Ω(τ) will provide the positions of channel impulses        relative to the coarse peak, n_(peak). Theoretically, first peak        will correspond to LOS path. Based on information about the        propagation environment which could be encoded in the        transmission from the base-station, it is possible to control        τ_(max). For example, if the delay-spread is large, then τ_(max)        can be chosen to be larger (e.g. 10) and if it is less then        τ_(max) can be chosen as a smaller value (e.g. 4).

Combination Methods:

Apart from the standalone methods discussed above, numerous othercombination methods are possible. Combination of schemes based on SNR onchip is an effective method. The following describes a list ofcombination schemes that can be realized in practice:

-   -   1. For chipSNR less than chipSNRRef, pick method 12(d) to choose        noise singular values. Otherwise choose method 12(a).    -   2. For chipSNR greater than chipSNRRef, pick method 12(d) to        choose noise singular values and estimate peak position.        Otherwise, use direct peak estimation techniques (such as peak        interpolation, peak shape) starting from the cross-correlation        function z[n].    -   3. For chipSNR less than chipSNRRef, pick method 12(e) to choose        noise singular values.

Otherwise choose method 12(a).

A typical value of chipSNRRef is 10 dB.

Computation of Position

The location of the receiver unit is determined by the positioningengine available either on the terminal unit or the server. The receivercan use the range measurements from the system or combine the systemrange measurements with any of the measurements from other signals ofopportunity. A sufficient set of range measurements yields a positionfix provided that the measurements derive from known locations. Therange equation in 3D space is given by

r _(i)=√{square root over ((x _(i) −X)²+(y _(i) −Y)²+(z _(i) −Z)²)}.

The location of the transmitters is given by (x_(i), y_(i), z_(i)) andthe unknown location of the mobile units is given by (X, Y, Z) in somelocal coordinate frame. Three or more transmitters produce three or morerange measurements that are used to compute a fix. The measurement has areceiver time bias additive term as well, because the receiver time isnot synchronized to the WAPS timing.

R _(i) =r _(i) +cΔt.

This equation is referred to later as “Pseudorange MeasurementEquation”. Note that the time bias is common because the transmittersare timing synchronized. The pseudoranges must be corrected for transmittiming corrections which are available from the data stream embedded inthe transmission from each transmitter. This delta time bias creates anew unknown parameter, so a minimum of four measurements are used for asolution. A barometric altimeter measurement provides the neededinformation for a solution as Baro=(z_(b)−Z).

One method of solving these non-linear simultaneous equations is tolinearize the problem at an arbitrary initial point and then iterativelyfinding corrections to this initial position to iteratively leads to thefinal solution.

This method uses an initial guess for the X, Y, Z solution, so thecentroid of the transmitters is used as

$\left( {X_{0},Y_{0},Z_{0}} \right) = {\left( {1/n} \right){\sum\limits_{i = 1}^{n}{\left( {x_{i},y_{i},z_{i}} \right).}}}$

The final position solution is assumed to be of the form(X,Y,Z,Δt)=(X₀,Y₀,Z₀,Δt₀=0)+(dX,dY,dZ,dΔt)

The geometric range can be expanded in a Taylor series about(X,Y,Z,Δt)=(X₀,Y₀,Z₀,Δt₀)

$\begin{matrix}{R_{i} = {\sqrt{\left( {x_{i} - X} \right)^{2} + \left( {y_{i} - Y} \right)^{2} + \left( {z_{i} - Z} \right)^{2}} + {c\; \Delta \; t}}} \\{= {\sqrt{\left( {x_{i} - X_{0}} \right)^{2} + \left( {y_{i} - Y_{0}} \right)^{2} + \left( {z_{i} - Z_{0}} \right)^{2}} +}} \\{\left. {{c\; \Delta \; t_{0}} + \frac{\partial r}{\partial x}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta \; t_{0}}})}{{dX} + \frac{\partial r}{\partial y}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta \; t_{0}}})}{{dY} +} \right.} \\{\left. \frac{\partial r}{\partial z} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta \; t_{0}}})}{{dZ} + {c\; d\; \Delta \; t}} \right.} \\{= \left. {{\hat{r}}_{i} + \frac{\partial r}{\partial x}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta \; t_{0}}})}{{dX} + \frac{{\partial r}\;}{\partial y}} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta \; t_{0}}})}{{dY} +} \right.} \\{\left. \frac{\partial r}{\partial z} \middle| {}_{({X_{0},Y_{0},Z_{0},{\Delta \; t_{0}}})}{{dZ} + {c\; d\; \Delta \; t}} \right.}\end{matrix}$

where the estimated ranges are computed as

{circumflex over (r)} _(i)=√{square root over ((x _(i) −X ₀)²+(y _(i) −Y₀)²+(z _(i) −Z ₀)²)}.

and the partial derivatives are given by

∂R/∂x=∂r/∂x=(x _(i) −X)/r _(i) ∂R/Δt=c

∂R/∂y=∂r/∂y=(y _(i) −Y)/r _(i)

∂R/∂z=∂r/∂z=(z _(i) −Z)/r _(i).

In this embodiment, four linear equations with four unknowns are shown.Additional range estimates would produce more rows in the matrix. Theresult is the set of equations

${\begin{bmatrix}{\left( {x_{1} - X_{0}} \right)/{\hat{r}}_{1}} & {\left( {y_{1} - X_{0}} \right)/{\hat{r}}_{1}} & {\left( {z_{1} - Z_{0}} \right)/{\hat{r}}_{1}} & 1 \\{\left( {x_{2} - X_{0}} \right)/{\hat{r}}_{2}} & {\left( {y_{2} - Y_{0}} \right)/{\hat{r}}_{2}} & {\left( {z_{2} - Z_{0}} \right)/{\hat{r}}_{1}} & 1 \\{\left( {x_{3} - X_{0}} \right)/{\hat{r}}_{3}} & {\left( {y_{3} - Y_{0}} \right)/{\hat{r}}_{3}} & {\left( {z_{3} - Z_{0}} \right)/{\hat{r}}_{1}} & 1 \\0 & 0 & 1 & 0\end{bmatrix} \times \begin{bmatrix}{\delta \; X} \\{\delta \; Y} \\{\delta \; Z} \\{c\; \delta \; \Delta \; t}\end{bmatrix}} = {\quad\begin{bmatrix}{R_{1} - {\hat{r}}_{1}} \\{R_{2} - {\hat{r}}_{2}} \\{R_{3} - {\hat{r}}_{3}} \\{z_{b} - Z_{0}}\end{bmatrix}}$

The last row of the observation matrix represents the barometricaltimeter measurement. The column of three 1 represents the same timebias on all three ranges. These equation are in the form of Ax=b. Thesolution x=A⁻¹*b. Note that in the absence of a barometer measurement,one more additional measurement would add an additional row similar torows 1 to 3 of the matrix above. This additional measurement wouldenable estimation of the altitude of the receiver. Note that when thereare more measurements available than the number of unknowns, then thesolution would be based on the pseudoinverse of A given byA₊=(A^(T)A)⁻¹A^(T) and the least square solution is given by x=A₊ ⁻¹ b.When the quality of measurements are not equal, the optimal way ofsolving the equations Ax=b in the least square sense is to use a weightproportional to the SNR for the error from each equation. This leads toa solution x=A₊ ⁻¹ b with A₊=(A^(T) WA)⁻¹A^(T)W. The diagonal weightingmatrix W formed by the weight proportional to the noise variance of themeasurements. The solution of these equations produces a deltacorrection to the X, Y, Z and delta time estimates, such that

$\begin{bmatrix}X_{1} \\Y_{1} \\Z_{1} \\{\Delta \; t_{1}}\end{bmatrix} = {\begin{bmatrix}X_{0} \\Y_{0} \\Z_{0} \\{\Delta \; t_{0}}\end{bmatrix} + {\begin{bmatrix}{\delta \; X} \\{\delta \; Y} \\{\delta \; Z} \\{\delta \; \Delta \; t}\end{bmatrix}.}}$

This completes the first iteration of the method. The updated positionand time bias estimates replace initial guess and the algorithm continueuntil the delta parameters are below some threshold value. A typicalstopping point would be for the norm of the delta values are below acertain threshold (for example, one meter).

The system of linearized equations in the GPS is solved using leastsquares and an initial guess about the location of the user such thatthe algorithm converges to the final user location. The linearization isbased on the fundamental assumption that the distance between thesatellites and the user position is larger than the distance between theuser position on the earth and the guessed position. For the same set ofequations to work in a terrestrial environment (with small geometry),the initial guess can be based on the centroid (as above), a point closeto the transmitter from which the received signal is the strongest, orobtained by a direct method which gives a closed form solution by meansof a sequence of formulae with no iterations. When the initial guess isa centroid or a point close to the transmitter from which the receivedsignal is the strongest, the initial guess is improved using a leastsquares method. When the initial guess is obtained by a direct methodwhich gives a closed form solution by means of a sequence of formulaewith no iterations, the initial solution itself is the final solutionand it is improved using least squares only when there are moremeasurements (and hence equations) than unknowns with individualmeasurements weighted by using the expected errors in those measurements(which are obtained from such parameters as signal strength andelevation angle). Further, if a sequence of measurements is to beprocessed in time, a solution obtained as above may be fed to a Kalmanfilter to obtain an optimal solution “trajectory”.

Another approach that overcomes the linearization problem in terrestrialcases involves formulating the set of equations as a non-linearminimization problem (specifically as a weighted non-linear leastsquares problem). Specifically, the non-linear objective function to beminimized is defined as

${f\left( {X,Y,Z,{\Delta \; t}} \right)} = {\sum\limits_{i = 0}^{N - 1}{W_{i} \times \left\lbrack {R_{i} - \sqrt{\left( {x_{i} - X} \right)^{2} + \left( {y_{i} - Y} \right)^{2} + \left( {z_{i} - Z} \right)^{2}} - {\Delta \; t}} \right\rbrack^{2}}}$

The weights W_(i) are chosen to be inversely proportional to the SNR ofthe measured ranges R_(i). The best estimate of the receiver location isobtained as the set of (X,Y,Z,Δt) that minimizes the objective function.When barometer or other altitude aiding is available then the objectivefunction gets modified to

${f\left( {X,Y,{Z = Z_{baro}},{\Delta \; t}} \right)} = {\sum\limits_{i = 0}^{N - 1}{W_{i} \times \left\lbrack {R_{i} - \sqrt{\left( {x_{i} - X} \right)^{2} + \left( {y_{i} - Y} \right)^{2} + \left( {z_{i} - Z_{baro}} \right)^{2}} - {\Delta \; t}} \right\rbrack^{2}}}$

The position solution based on this method will be more stable androbust, particularly under small geometry terrestrial systemconfiguration. In this configuration, small changes in receivercoordinates significantly changes the observation matrix and sometimesleads to lack of convergence of the linearized iterations. Convergenceto a local minimum or divergence occurs more often due to residual biasin the measurements which affects the shape of the objective function sothat local minima can be present. Residual bias can be quite common inindoor/urban canyon environments. The non-linear formulation above makesthe position algorithm robust to measurement bias besides overcoming thesmall geometry linearization problem.

One approach to perform the minimization of the functionf to obtainoptimal X, Y, Z is to use a genetic algorithm (such as differentialevolution) to find the global minimum of the function. The use of suchan algorithm enables the solution to avoid local minima that occur insmall geometry terrestrial positioning when multi-path bias is presentin the range measurements.

Irrespective of whether linearized least squares or non-linear leastsquares method is used to solve the pseudo-range measurement equations,it is important for a quality metric to be provided along with aposition estimate. The position quality metric should be a function ofthe pseudo-range measurement equation residuals, the quality of themeasurements as well as the geometry of the towers relative to theestimated position. The pseudo-range measurement residual for the ithtower measurement is given by

PR_(res,i) =R _(i)−√{square root over ((x _(i) −X)²+(y _(i) −Y)²+(z _(i)−Z)²)}+cΔt)

The average weighted rms pseudo-range residual is given by

${PR}_{res} = \sqrt{\left( \frac{\sum\limits_{i}{W_{i} \times {PR}_{{res},i}^{2}}}{\sum\limits_{i}W_{i}} \right)}$

The HDOP, VDOP, PDOP are defined from the diagonal elements ofH=(A^(T)A)⁻¹A^(T) as

HDOP=√{square root over (H(1,1)+H(2,2))}

VDOP=H(3,3)

PDOP=√{square root over (H(1,1)+H(2,2)+H(3,3))}

The pseudo-range RMS (root-mean-square) error at a particular SNR isgiven by

PRE_(th)=ƒ(√{square root over (SNR)})

where ƒ is generally a non-linear monotonic decreasing function of itsargument. The function ƒ can be derived analytically for a particularreceiver configuration as a function of signal BW and receiver BW oralternatively, found from simulation as a table mapping SNR to rangeerror.

The quality metric for 2-D position is defined as

QM_(2-D)=HDOP×√{square root over (PR_(res) ²+PRE_(th) ²)}×α

Similarly, the quality metric for the altitude and 3-D position is givenby

QM_(alt)=VDOP×√{square root over (PR_(res) ²+PRE_(th) ²)}×α

QM_(3-D)=PDOP×√{square root over (PR_(res) ²+PRE_(th) ²)}×α

The quantity α is chosen based on the level of confidence desired. Forexample, a value of 3 would be used to obtain 95% confidence, while avalue of 1 would be used for 68% confidence.

Another method of positioning using the WAPS system involves the use ofa WAPS reference receiver in a differential scheme. As shown in“Differential Wide Area Positioning System” and discussed in the contextof timing synchronization, the time-stamped reference receivermeasurements along with the latitude, longitude, altitude of the WAPStowers and the reference receiver can be used to determine the timingdelta between WAPS tower transmissions at the specific time-stamp. Oncethe timing delta between transmitters is known, the range equations canbe reduced to have a single common time bias again. The WAPS receiverthen can avoid demodulation of the WAPS data stream (for example, toextract the timing corrections from the data stream). The WAPS receivermeasurements can be sent to the server and the position can then becomputed at the server or, alternatively, the reference receivermeasurements can be relayed to the WAPS receiver and the position can becomputed there. It is assumed that the latitude, longitude and altitudeof the WAPS towers is already known/available for use in the positioncomputation. In the case that the WAPS data stream is secure, thisdifferential system can avoid the need to extract data from the securedata stream for timing correction purposes.

Another alternative method for obtaining positioning from the WAPSsystem uses RSSI finger-printing techniques. A database of WAPS towertransmit powers/locations and RSSI levels is built up for a given targetarea based on training measurements in the area for which positioning isrequired. Note that RSSI database can also be augmented with Angle ofArrival (AOA) information to improve the solution. The WAPS receiverRSSI measurements (and possibly AOA measurements) are then used to lookup this database to obtain a location estimate. An alternative method ofusing the WAPS RSSI measurements would be to translate the measurementsinto a range estimate using a propagation model (or simpleextrapolation/interpolation techniques) and then use tri-lateration todetermine the position. Note that the RSSI measurements in thesefinger-printing techniques can be replaced by any other measurementsthat can be translated to range.

An alternative method of computing position using the WAPSinfrastructure uses a blind method for obtaining positioning from theWAPS system without prior knowledge of the WAPS tower locations. In thismethod, the approximate location of the WAPS towers are determined byfield measurement (for example, by measuring RSSI from many anglesaround the WAPS tower at GNSS tagged locations and then using a weightedaverage based on RSSI of these locations to estimate WAPS towerlocations). Then, any of the RSSI finger-printing methods can be used todetermine position (for example, as described in the above paragraph).

An alternative method of computing position using the WAPSinfrastructure can be used for computing position offline. The positioncomputation involves storing the sample segments of the WAPS signal (forexample, the stored data maybe I data at low IF or IQ data at baseband)from the WAPS receiver along with optionally an approximate position anda WAPS time tag. Note that it is enough to store enough samples to beable to acquire the signal. The samples are processed at a later time tosearch, acquire and compute range to WAPS towers. The method may useoffline data to look-up tower locations and timing correctioninformation that may be stored in a central database on a server. Thismethod of offline position computation provides the ability to supportWAPS positioning at the cost of only memory on the device. The otheradvantage of this method is the time taken for storing the WAPS IQ datais very short, making it convenient for applications that need to tagposition quickly, but the exact position is not requiredinstantaneously. One possible application for this method can be forgeo-tagging of photographs.

Another approach to positioning uses carrier phase measurements inaddition to the code phase measurements indicated above. The carrierphase measurements can be written as: ϕ_(i)(t₀)=r_(i)(t₀)+N_(i)λ+Δt.Various techniques can be used to resolve the integer ambiguity N_(i) inthe carrier phase measurements. Code phase measurements, measurements atmultiple frequencies and/or other methods can be used to resolve theambiguities. Subsequently, the carrier phase measurements at time t_(k)can provide accurate tracking of position starting from an accurateinitial position. The carrier phase measurements at future times can bewritten as ϕ_(i)(t_(k))=r_(i)(t_(k))+N_(i)λ+Δt. The N_(i) do not changeas long as the carrier phase measurements do not have cycle slips (i.e.the signals should be tracked with continuous phase lock) and the newlocations can be computed using least squares. Alternatively, thesemeasurements can be used in a Kalman filter to update the new positionstate. If phase lock is lost, new values of integer ambiguity need tocalculated. Another approach uses differential positioning relative to areference receiver as described above. Differential positioning can bedone using either code or carrier measurements or a combination of both.Single difference observables are computed for code and carrier phase bysubtracting measurements of the same towers from reference receiver rand receiver s as

$R_{sr}^{i} = {\underset{\underset{\underset{difference}{{geometrical}\mspace{14mu} {range}}}{}}{\rho_{s}^{i} - \rho_{r}^{i}} + \underset{\underset{\underset{{between}\mspace{14mu} {clocks}}{{time}\mspace{14mu} {difference}}}{}}{c\left( {{dt}_{s} - {dt}_{r}} \right)} + \left( {ɛ_{R,s} - ɛ_{R,r}} \right)}$$\Phi_{sr}^{i} = {\underset{\underset{\underset{difference}{{geometrical}\mspace{14mu} {range}}}{}}{\rho_{s}^{i} - \rho_{r}^{i}} + \underset{\underset{\underset{{between}\mspace{14mu} {clocks}}{{time}\mspace{14mu} {difference}}}{}}{c\left( {{dt}_{s} - {dt}_{r}} \right)} + \underset{\underset{\underset{{phase}\mspace{14mu} {measurement}}{{integer}\mspace{14mu} {ambiguity}\mspace{14mu} i\; n}}{}}{\lambda \left( {N_{s}^{i} - N_{r}^{i}} \right)} + {\left( {ɛ_{\varphi,s} - ɛ_{\varphi,r}} \right).}}$

Note that any timing error in the transmitter does not appear in theseobservables and thus allows position solutions even when the system isasynchronous or imperfectly synchronized. In addition, any troposphericdelay error in measurements nearly cancels out since the troposphericdelay is likely to be correlated in the local area for short baselines(i.e., distances between reference receiver r and receiver s). Acommunication channel is used to send the range and carrier measurementsfrom the reference receiver r to the receiver s for positioncomputation. Or, alternatively, the receiver s and receiver r need tocommunicate the range and carrier to the server for positioncomputation. In any position solution method, the height of a receivercan be determined using placement on a terrain map or barometricsensing. Using placement on a map, during trilateration the location ofthe user can be constrained to be on a terrain based on a terraindatabase and the height of the user determined. The height of the usercan also be constrained to be within a certain height above the terrain.For example, based on the tallest building in the area, the maximumaltitude above terrain can be constrained. This type of constraint canimprove the quality of the height solution (for example, by eliminatingthe ambiguous solution that is sometimes produced when using biasedrange measurements). In addition, if indoor building maps are available,the information (along with associated constraints on possible userlocations) can be used to aid the position solution For example,physical restrictions can be used to constrain the user motion model,and thereby improve the quality of the tracking Kalman position filter.Another usage of building maps is to determine/estimate the quality of aparticular tower's range measurement based on the physical environmentfrom the tower to the indoor location. A better estimate of rangequality can be used to weight the position computation leading to betterposition estimates. When using a barometric sensor, a calibratedbarometric sensor can be used to measure the pressure differences as thereceiver terminal is moved up or down in altitude. This is compared witha calibrated value for the pressure on different altitudes or an averagevalue to determine the height of the receiver. In computing the positionsolution, when additional measurements greater that the minimum threemeasurements required for two-dimensional position are available,receiver integrity monitoring based on a check of consistency ofmeasurements is used to eliminate “outlier” measurements. The “outlier”measurements could be due to loss of timing synchronization at thetransmitter or due to the channel effects such as multipath.

Altimeter-Based Approach for Determining Elevation

The WAPS system of an embodiment includes altimeters (pressure sensor)to aid in the determination of user elevation. The only informationavailable from a pressure sensor is the atmospheric pressure at the timeand place of the measurement. In order to translate this into anestimate of the elevation of the sensor, a number of additional piecesof information are required. There is a standard formula for relatingpressure to elevation, based upon the weight of a column of air, asfollows:

${z_{1} - z_{2}} = {{- \frac{RT}{g}}{\ln \left( \frac{P_{1}}{P_{2}} \right)}}$

where z₁ and z₂ are two elevations, and P₁ and P₂ are the pressures atthose elevations, and T is the temperature of the air (in K). R=287.052m²/Ks² is the gas constant and g=9.80665 m/s² is the acceleration due togravity. Note that this formula provides relative information,determining the difference in elevation for a difference in pressure.This formula is generally used with z₂=0, so that P₂ is the sea levelpressure. Because sea level air pressure varies significantly withweather conditions and with location, the sea level pressure is neededin addition to the temperature and pressure at the site where elevationis to be determined. When applying standard atmosphere conditions, withT=15 C and P=101,325 Pa, it is found that a 1 m increase in elevationcorresponds to a 12.01 Pa decrease in pressure.

Thus, to determine elevation with a resolution of 1 m, sea levelpressure must be known with accuracy significantly finer than 36 Pa. Itis also worth noting that because T is measured in Kelvin, a 3° C. (orK) error in temperature will correspond to approximately a 1% error inelevation. This can become significant when determining elevationsignificantly above sea level, and when trying to resolve upper floorsin a high rise building. Thus, for determining elevation with aresolution of 1 m, pressure sensors with high accuracy and resolutionare needed. In order to fit in a mobile device, these sensors should below cost, low power and small size. Note that commercial weather gradesensors do not provide this level of accuracy or resolution and are notupdated at a rate required for determining elevation.

The key to determining elevation to 1 m accuracy is to have a system forproviding reference pressure information that is local enough andaccurate enough. It must be able to provide measurements that are closeto the unknown location in temperature, and close in distance andtime—to capture changing weather conditions; and finally, must besufficiently accurate. Thus, the elevation determining system of anembodiment includes but is not limited to the following elements: amobile sensor that determines pressure and temperature at the unknownlocation with sufficient accuracy; an array of reference sensors thatdetermine pressure and temperature at known locations with sufficientaccuracy, and are sufficiently close to the unknown location; aninterpolation-based estimation algorithm which inputs all referencesensor data, reference sensor locations and other augmentinginformation, and generates an accurate reference pressure estimation ata location of interest within the WAPS network; a communications linkbetween the reference sensors and the mobile sensors to provide thereference information in a sufficiently timely fashion. Each of theseelements is described in detail below.

FIG. 33 is a block diagram of a reference elevation pressure system,under an embodiment. Generally, the reference elevation pressure system,or reference system, includes a reference sensor array comprising atleast one set of reference sensor units. Each set of reference sensorunits includes at least one reference sensor unit positioned at a knownlocation. The system also includes a remote receiver comprising orcoupled to an atmospheric sensor that collects atmospheric data at aposition of the remote receiver. A positioning application running on aprocessor is coupled to or is a component of the remote receiver. Thepositioning application generates a reference pressure estimate at theposition of the remote receiver using the atmospheric data and referencedata from the reference sensor unit(s) of the reference sensor array.The positioning application computes an elevation of the remote receiverusing the reference pressure estimate.

More specifically, the reference elevation pressure system includes amobile sensor that determines pressure and temperature at the unknownlocation with sufficient accuracy, and the mobile sensor is a componentof or coupled to the remote receiver. The system includes a referencesensor array that comprises at least one reference sensor unit thataccurately determines pressure and temperature at a known location thatis appropriate to a location of the remote receiver. The referencesensor units communicate with the remote receiver and/or an intermediatedevice (e.g., server, repeater, etc.) (not shown) to provide thereference information. The system comprises a positioning applicationthat, in an embodiment, is an interpolation-based estimation algorithmwhich inputs all reference sensor data, reference sensor locations andother augmenting information, and generates a relatively accuratereference pressure estimation at a location of interest. The positioningapplication can be a component of the remote receiver, can be hosted ona remote server or other processing device, or can be distributedbetween the remote receiver and a remote processing device.

FIG. 34 is a block diagram of the WAPS integrating the referenceelevation pressure system, under an embodiment. As described herein, theWAPS includes a network of synchronized beacons, receiver units thatacquire and track the beacons and/or Global Positioning System (GPS)satellites (and optionally have a location computation engine), and aserver that comprises an index of the towers, a billing interface, aproprietary encryption algorithm (and optionally a location computationengine). The system operates in the licensed/unlicensed bands ofoperation and transmits a proprietary waveform for the purposes oflocation and navigation purposes. The WAPS system can be used inconjunction with other positioning systems or sensor systems in order toprovide more accurate location solutions. Note that the elevation of theremote receiver computed using the reference pressure estimate can beused either explicitly as an altitude estimate or implicitly to aid theposition calculation in any position location system.

One example system integrates the reference elevation pressure systemwith the WAPS. Generally, the integrated system comprises a terrestrialtransmitter network including transmitters that broadcast positioningsignals comprising at least ranging signals and positioning systeminformation. A ranging signal comprises information used to measure adistance to a transmitter broadcasting the ranging signal. The systemincludes a reference sensor array comprising at least one referencesensor unit positioned at a known location. The remote receivercomprises or is coupled to an atmospheric sensor that collectsatmospheric data at a position of the remote receiver. A positioningapplication running on a processor is coupled to or is a component ofthe remote receiver. The positioning application generates a referencepressure estimate at the position of the remote receiver using theatmospheric data and reference data from a set of reference sensor unitsof the reference sensor array. The positioning application computes theposition of the remote receiver, which includes an elevation, using thereference pressure estimate and information derived from at least one ofthe positioning signals and satellite signals that are signals of asatellite-based positioning system.

More specifically, this integrated system includes a mobile sensor thatdetermines pressure and temperature at the unknown location withsufficient accuracy. The mobile sensor is a component of or coupled tothe remote receiver, but is not so limited. The system includes areference sensor array that comprises at least one reference sensor unitthat accurately determines pressure and temperature at a known locationthat is appropriate to a location of the remote receiver. The referencesensor units communicate with the remote receiver and/or an intermediatedevice (e.g., server, repeater, etc.) (not shown) to provide thereference information. The reference sensor units can be collocated withone or more WAPS transmitters and/or can be separately located at otherknown locations. The system comprises a positioning application that, inan embodiment, is an interpolation-based estimation algorithm whichinputs all reference sensor data, reference sensor locations and otheraugmenting information, and generates a reference pressure estimation ata location of interest. The positioning application can be a componentof the remote receiver, can be hosted on the WAPS server or otherprocessing device, or can be distributed between the remote receiver andthe WAPS server.

As noted above, the mobile sensor should be able to determine pressurewith a resolution and accuracy that is significantly finer than 36 Pa,Many pressure sensors have built-in temperature sensors in order toprovide compensation for non-ideal sensor performance, but due toself-heating effects, these sensors may not provide a sufficientlyaccurate measure of outside air temperature. Even in cases whereaccurate sensors are not available commercially, if sensors withadequate resolution are available, they can be used for the purposes ofaltitude estimation at the floor level. The mobile sensor of anembodiment determines the reference pressure data with a resolutionapproximately less than 36 Pascal, and determines the temperature datawith a resolution at least one of equal to and less than approximately 3degrees Celsius.

These sensors have inherent short term and long term stability issueswhich may be corrected by modest filtering techniques such as averaginga few samples. Each sensor may also have an offset that may vary withtemperature which needs to be calibrated or compensated by means of alook up table, for example.

With sufficient calibration, these sensors should provide the accuracyneeded. Some sensors may also be sensitive to high rates of motion. Someheuristic rules may be used to limit use of pressure information whenhigh velocities or acceleration are recognized. However, high velocitiesare rarely experienced in indoor environments. When traveling at highspeeds, GPS positioning and map data will typically provide sufficientvertical position information.

It should also be noted that the sensor should be mounted in a mannerthat exposes it to outside air, but not wind, draft, or other airmovement. A mounting or positioning internal to a typical consumerproduct should produce acceptable results. The battery compartment andconnectors provide an indirect path for outside air to get to thesensor, while preventing any direct air movement. However, a water proofdevice would need special provisions to provide the sensor with accessto the outside.

The reference sensors will be deployed in much smaller volumes, and atdedicated sites, so relatively better accuracy can be obtained in thereference system, making it possible to allocate the bulk of the overallerror budget to the mobile sensors. Existing markets for absolutepressure sensors, such as weather and aircraft altimeters, do not havethe same high accuracy requirements as the application of an embodiment.In the reference application, an embodiment uses multiple sensors, bothfor redundancy and for improved accuracy by averaging theirmeasurements. In addition, the sensors may be packaged so as to limitthe temperature range to which the sensor is exposed and optimallycalibrate the sensor for this limited temperature range.

The reference system should average or otherwise filter individualmeasurements to improve accuracy with a time scale in the order of a fewseconds to a few minutes. The height of the reference sensor should bemeasured to a ‘cm’ level accuracy; the outside air temperature should becontinuously measured and logged; the sensor should be exposed tooutside air in order to measure the air pressure, but must not besubject to wind, drafts, or other significant air movement (baffles orother packaging can be used to direct air along an indirect path to thesensor); the sensor should not be sealed in a water proof enclosure, asthis can prevent measurement of outside air pressure. The referencesensor of an embodiment determines the reference pressure data with aresolution approximately less than 36 Pascal, and determines thetemperature data with a resolution at least one of equal to and lessthan approximately 3 degrees Celsius.

An embodiment enables interpolation-based reference pressure estimation.Given the pressure and temperature measurements at each WAPS transmittertower, as well as the tower location and other augmenting information,an embodiment predicts the sea level atmospheric pressure at the mobileuser location as the reference value for user height estimation.Therefore, an atmospheric pressure surface gradient model is generatedand the pressure measurements at each tower site serve as the sampledata for local modification of the model. Therefore, this estimationalgorithm calibrates comparable reference pressure accuracy at the userlocation as the direct measurements captured at the beacon tower.

A description of a formulation of this interpolation is described below.Within one of the WAPS network, given reference barometric pressuresensors at n transmitter towers, the equivalent sea level atmosphericpressure is estimated based on the reference sensor outputs. This isdone in two steps, but is not so limited.

As a first step, given the reference sensor height h_(i) (in meters)above sea level at transmitter tower i, and the pressure p_(i) (inPascal) and temperature T_(i) (in Kelvin) readings from the referencesensor, the equivalent sea level atmospheric pressure P_(i) (in Pascal)is calculated at location with latitude x_(i) and longitude y_(i) (indegrees), using the formula below:

${P_{i} = {p_{i}e^{\frac{{gh}_{i}}{{RT}_{i}}}}},$

where g is the gravitational acceleration constant and R is the specificgas constant for air. As a second step, after calculating the equivalentsea level atmospheric pressures at all n transmitter locations of theWAPS network, and obtaining the latitude x₀ and longitude y₀ informationof the user with WAPS, the equivalent sea level pressure is estimated atthe user location P₀ with the formula below: P₀=Σ_(i=1) ^(n) W_(i)P_(i),where W_(i)=W_(i) (x₀, y₀, x_(i), y_(i)) is the weighting functiondepending on both the user location and the reference site i location.

The communications link of an embodiment provides the information usedby the mobile sensor. An embodiment broadcasts pressure updates onceevery few seconds to few minutes but is not so limited.

If the reference system broadcasts reference information infrequently,the mobile unit performs at least one of the following: continuouslymonitors the broadcasts to receive and store the last information incase it is needed before the next broadcast; waits for the nextbroadcast before computing a new elevation; “pulls” or queries thereference system for the latest information when needed. The Pullapproach of an embodiment, rather than having the reference systemsbroadcast the information, minimizes system bandwidth. However, the Pulluses two-way communications between the reference system and the mobile,and since multiple reference sites would be used for any mobilecalculation, so it requires the mobile to determine which referencesites it should query. A good compromise to minimize monitoring by themobile, while keeping latency low, has the reference system broadcastits data more frequently than the time it takes to update themeasurement.

An embodiment includes two possible approaches for the informationcontent. A first approach has the mobile perform all of thecalculations, in which case the information sent by the referenceincludes but is not limited to the following: reference location(latitude and longitude) with one meter accuracy; height of referencesensor with 0.1-0.2 m accuracy; measured temperature of air at referencesite (after some filtering); measured pressure of air at reference site(after filtering, sensor temperature compensation, and any other localcalibration such as offset), with one Pa accuracy; and a measure ofconfidence.

Alternatively, the reference site can use its temperature and pressuremeasurements to compute an equivalent sea level pressure. If thisapproach is used, the list of information to be broadcast includes butis not limited to the following: reference location (latitude andlongitude) with one meter accuracy; height of reference sensor with0.1-0.2 m accuracy; computed equivalent sea level pressure at referencesite (with one Pa accuracy); a measure of confidence.

An embodiment also reduces the bits of data transmitted but broadcastseach piece of data relative to some known constant. For example, thereference sites are relatively close to the mobile site, so only thefractional degrees of latitude and longitude may be transmitted, leavingthe integer part to be assumed. Similarly, air pressure, althoughtypically on the order of 10⁵ Pascals, only varies by a few thousand Pafrom the standard atmosphere. Thus, an embodiment broadcasts the offsetfrom standard atmospheric pressure to reduce the bandwidth overbroadcasting the absolute pressure.

Latitude and longitude, as obtained from GPS or similar systems, are notparticularly useful in urban applications. Instead a database is neededto map latitude and longitude into street addresses. Elevation has asimilar limitation in the vertical dimension. The useful parameter iswhich floor a person is on. This can be determined accurately fromelevation information if there is access to a database of the groundlevel elevation and the height of each floor in a building. For lowbuildings up to approximately 3 stories, it may be sufficient to knowground level elevation from mapping or similar databases, and estimatefloor height. For taller buildings more accurate information about floorheight will be needed.

This presents an opportunity to implement smart learning algorithms. Forexample, one can assume that cell phones will be carried between 1 m and2 m from the floor. Thus, the system of an embodiment can accumulate theelevations of many cell phones in a building, wherein the data isexpected to cluster around 1.5 m from each floor. With enough data, itis possible to develop confidence as to the height of each floor in thebuilding. Thus, the database could be learned and refined over time.Such an algorithm becomes more complicated in buildings with ramps, ormezzanines between floors, but may still generate useful data for themajority of buildings.

The sensor offsets, and potentially other parameters, can be calibratedat the time of manufacture. This should be possible by cycling thesensors through a range of temperature and pressure with a known goodsensor providing reference information. It is likely that thesecalibration parameters will slowly drift with age. Therefore, anembodiment uses an algorithm to gradually update the calibration overtime (e.g., algorithm recognizes when a sensor is stationary at a knownheight and updates the calibration table under those conditions).

In addition to the general application of determining a person'slocation, an embodiment may include specialized applications that usemore precise relative elevation information, while not needing absoluteelevation information. For example, finding a downed firefighter in abuilding requires that the position of the downed person relative to therescue party be known precisely, but neither absolute position is asimportant. Additional precision in relative positioning would bepossible by having an extra manual step at the beginning of theapplication. For example, all firefighters could initialize theretrackers at a known location, such as the entrance to the building,before they enter. Their position relative to that point, and thusrelative to each other could be determined quite accurately for a periodof time, even if absolute elevation is not accurate, and weather relatedpressure changes cannot be completely compensated for. Similarly, ashopping related application that requires more precision than availablefrom the absolute measurements could be implemented by having the userpress a button at a known point in the mall. Their position relative tothat point could then be determined quite accurately for a period oftime.

Alternatively, a mobile beacon can be utilized as a local reference toprovide more accuracy in a particular location. For example, a shoppingmall could have its own reference sensor, to provide more accuracywithin the mall. Similarly, a fire truck could be equipped with areference sensor to provide local reference information at the scene ofa fire.

Low cost pressure sensors have a problem in that they have an offsetfrom the correct reading. Experiments have shown that this offset isquite stable on time scales of weeks to months. However, it is likelythat this offset will slowly drift with time over a period of manymonths to years. While it is straightforward to measure this offset, andcompensate for it at the time of manufacture, it is unlikely that thecompensation will stay accurate for the life of the product. Therefore,a means of recalibrating in the field is required.

The sensor of an embodiment can be recalibrated if it is at a knownelevation and the atmospheric pressure is known. The embodimentidentifies practical situations where the sensor will be at a knownelevation. For example, if the sensor is in a device that has GPScapability, and the GPS satellites are being received with high signalstrength, the GPS derived altitude should be quite accurate.Accumulating the deviations from GPS altitude over time, under goodsignal conditions, can provide an estimate of the correction needed tothe sensor calibration.

Similarly, the sensor system can learn the user's habits and use thisinformation to later correct the calibration. For example, if the userconsistently places her phone in one place at night, the sensor canstart tracking the altitude at this location, perhaps at specific times,such as late night. Initially, these values would be accumulated andstored as the true altitude at that location. After several months, whenthe sensor determines that it is in the same location at the same timeof night, it could start to track deviations from the true altitudedetermined earlier. These deviations could then be accumulated to slowlygenerate a correction to the calibration. Because these approaches alsouse knowledge of current atmospheric pressure, they use referencepressure measurements provided by the WAPS network.

The standard process for determining altitude from pressure readingsinvolves converting the measurements at a reference location to theequivalent sea level pressure, and then using that to determine thealtitude of the unknown pressure sensor. The standard formula is:

${z = {{- \frac{RT}{g}}{\ln \left( \frac{P}{P_{0}} \right)}}},$

Note that a minus sign has been added, since height is conventionallymeasured as positive moving away from the surface of the earth. Inaddition, the logarithm has been corrected to ‘ln’ since this is anatural logarithm. This formula relates, z, the height above sea level,to the atmospheric temperature (T) and pressure (P) at that point, andthe sea level air pressure (P₀) below that point.

One additional problem with applying this formula is that the height isdirectly proportional to the temperature, a measured quantity not knownprecisely. This means that a 1% error in temperature will result in a 1%error in height. When used near sea level this will not be a significantproblem. However, when this formula is applied in tall buildings andespecially in higher elevation areas, such as Denver, a 1% error inheight may be significant when attempting to resolve floor levelelevation. For example, the elevation of Denver is about 1608 m. Thus, a1% error in temperature will result in an error in height above sealevel of 16 m. This is nearly 5 floors.

One way to avoid this sensitivity to temperature accuracy is torecognize that the formula above is actually a relative formula. That isthe formula can be generalized to:

${{z_{1} - z_{2}} = {{- \frac{RT}{g}}{\ln \left( \frac{P_{1}}{P_{2}} \right)}}},$

where z₁ and z₂ are any two elevations, and P₁ and P₂ are the pressuresat those elevations. It was only a matter of convention that z₂ was setto 0, and thus P₂ became the sea level pressure. Instead of using sealevel as the reference point, any convenient elevation could be used.For example, the mean elevation of the city would be reasonable, or themean elevation of the reference sensors used for collecting pressuredata would work. As long as a reference elevation is used that keeps theheight differences small, the impact of temperature error will beinsignificant. The only requirement is that all devices involved in thesystem know what reference elevation is being used. There is a standardformula that relates elevation of a point above the earth (z), theatmospheric temperature (T) and pressure (P) at that point, and the sealevel air pressure (P₀) below that point as

${z = {{- \frac{RT}{g}}{\ln \left( \frac{P}{P_{0}} \right)}}},$

This formula assumes that there is a column of air at constanttemperature between sea level and the point of interest. Therefore, thesea level pressure used is a virtual construct, and not necessarily thereal pressure at sea level, since the point of interest may not be neara true sea level. The standard process for determining elevation of anobject is a two step process. First sea level pressure is determined bymeasuring temperature and pressure at a point of known elevation, andthen inverting this formula to solve for P₀. Next, the temperature andpressure at the point of unknown elevation are measured, and thisformula is applied to determine the unknown elevation.

Implicit in this process is the assumption that only parameter ofinterest is the height of other objects above the same horizontallocation, as is typical for aircraft approaching an airfield, usingmeasurements at the airfield for reference. Typically, people interestedin height determination for other purposes have extended this concept todetermining the height in the general vicinity of a reference location,but not directly above it. This extension assumes that the sea levelpressure does not change between the location of interest in thevicinity and the reference location.

Thus, there are three assumptions in this process. A first assumption isthat the temperature is constant from the reference location to thevirtual sea level point below it. A second assumption is that thetemperature is constant from the point of interest to the virtual sealevel point below it. A third assumption is that the sea level pressureis the same at the reference location and the point of interest.However, since sea level pressure depends upon temperature, assumingthat the sea level pressure is the same at two locations implies thatthe temperature is the same at those locations. Thus, if differenttemperatures are measured at the reference location and point ofinterest, one of these assumptions has been violated. Measurements haveshown that even over distances of a few kilometers, there aredifferences in temperature and in pressure that can be significant forelevation determination.

The assumption of constant temperature over elevation changes at a givenlocation is part of the equilibrium model for the atmosphere, and isprobably necessary. The only alternative would be a full dynamic modelof the atmosphere, including the effects of wind, surface heating,convection, and turbulence. Atmospheric data suggest that at least onlarge distance scales, the constant temperature model is a very goodapproximation at elevations below 1 km. At higher elevations, a linearlapse rate is often applied.

An embodiment relaxes the assumption of constant sea level pressurebetween the reference location and the point of interest. A firstapproach of an embodiment takes the sea level pressure for the referencelocation determined as above, but further applies the ideal gas law toconvert this to a sea level pressure at a standard temperature. Thenassume that this sea level pressure at a standard temperature would bethe same at the point of interest. The temperature at the new locationwould then be used to convert this to the sea level pressure for thatlocation, and then apply the formula above to determine the elevation.

A second approach of an embodiment uses a network of reference locationsto determine the variation of equivalent sea level pressure withhorizontal location in real time. These multiple measurements are thencombined to determine a best estimate of the sea level pressure at thepoint of interest. There are at least two possible ways of determiningthe best estimate: a weighted average approach in which the weighting isa function of the horizontal distance from the particular referencepoint to the point of interest; a least square fit to create a secondorder surface that best fits the computed sea level pressures at thereference locations and can then be used to interpolate an estimate ofthe sea level pressure at the point of interest.

The two approaches described above can also be combined. That is, ateach reference location the sea level pressure at standard temperatureis determined, and these data are combined using one of the techniquesabove to generate a best estimate of the sea level pressure at standardtemperature at the point of interest.

Additionally, when using the altimeter, an embodiment recognizes suddenmovements in pressure such as the air conditioner changing state (e.g.,turning ON, etc.) or windows opening in a car by using application leveldata into the hardware or software filters that operate continuously onthe location and altimeter data.

Further, a wind gauge can be used at the beacon to determine thedirection of the wind flow, which is believed to be a indicator ofatmospheric pressure gradient. A wind gauge along with a compass can beused to determine the precise direction and level of wind flow which canthen be used to correct and/or filter our variations in the user'ssensor.

The per floor height of a given building can be determined by variousmethods including but not limited to a user walking the building throughthe stairs and collecting information about each floor, ramps etc. Inaddition an electronic diagram can be used to determine the relativeheight of each floor.

When the height is estimated based on either WAPS or the altimeter,information such as terrain, height of the building, height ofsurrounding buildings, etc. can be used to constrain the heightsolution.

Once an average pressure is known at a given location, along withhistorical reference pressure data collected from the reference sensorsover a long period of time (days, months, year), it can be used topredictably determine the height based on the pressure at that location(without calibration or user input).

In one embodiment, the height of the user can be computed on a remoteserver by using the data from the user's sensor and combining it withthe data from reference sensors. In this method, other information suchas building information, crowd sourced information, etc. can also beused to determine the user's precise altitude.

In case a user is in close proximity to another user whose height isknown, this information can be used to determine the unknown user'sheight.

In one embodiment of the network, the reference sensors need notnecessarily be co-located with the WAPS beacon. A finer or a coarsergrid of independent sensors with data connection to the server can beused for reference pressure measurement. The centralized server caneither send reference pressure information to the mobile or can instructthe transmitters with data that needs to be sent to the mobile as a partof the WAPS data stream.

In another embodiment, the WAPS system uses an additional simplifiedbeacon (supplemental beacon) that provides additional sensor informationsuch as pressure, temperature in a smaller area such as a building. Thistransmission may be synchronous or asynchronous to the main WAPS timingbeacons. Additionally, the supplemental beacon may either upload thesensor data to a centralized server from which it is disseminated to themobile units or transmit the data over a predefined set of PRN codeswhich can be demodulated by the WAPS mobile receiver.

The reference pressure network can be optimized based on accuracyrequirements and historic pressure variation data for a given localarea. For example, in cases where very accurate measurement is a must, areference sensor can be deployed in that building or a mall.

The WAPS beacon network along with the reference pressure data forms aclose network of accurate pressure and temperature measurement with veryshort time intervals which can be harnessed by other applications suchas geodesy.

The rate of change of pressure combined with data from other sensors canbe used to determine vertical velocity which can then be used todetermine if a user went through an elevator. This can be very useful inemergency situations and/or tracking applications.

In cases of sensors with lower resolution than needed to estimate floorheight, under static conditions, averaging the pressure measurementsover time can be used to obtain the user height based on reference data.

Hybrid Positioning and Information Exchange with Other Systems

The system of an embodiment can be combined with any ‘signal ofopportunity’, in order to provide positioning. Examples of a signal ofopportunity include, but are not limited to, one or more of thefollowing: GPS receivers; Galileo; Glonass; Analog or Digital TV Signal;signals from systems such as MediaFLO, W_(i)-Fi; FM signals; WiMax;cellular (UMTS, LTE, CDMA, GSM etc); bluetooth, and, LORAN and e-LORANreceivers.

Regardless of signal type, the signal of opportunity provides a rangemeasurement or a proxy for a range measurement, such as signal strength.This proxy for a range is weighed and combined appropriately to get anestimate for the location. The weighting may use the signal-to-noiseratio (SNR) of the received signals or, alternatively, use a metric thatdefines the environment of the receiver (e.g., knowledge of urban,suburban, rural environment from assistance data, whether the receiveris indoor or outdoor based on input from the application). This istypically done in those environments where the system of an embodimentis unavailable or signal coverage is limited. When using the SNR for aweight for a particular measurement the weight may simply be an inversefunction of the SNR (or any other function that provides lower weight tosignals with lower SNR) to allow optimal combination of the WAPSmeasurements as well as other system measurements to obtain a position.The final positioning solution may be calculated either by taking rangemeasurements from the additional signal sources and combining with theWAPS range measurements and deriving a position solution for latitude,longitude and height, or by taking the position measurements from theadditional sources/devices and the position measurements from the WAPSsystem and providing an optimized location solution using a combinationof these location measurements based on the position quality metric fromdifferent systems. The various configurations of obtaining a hybridsolution using WAPS measurements/WAPS position estimates are shown inFIG. 35, FIG. 36, and FIG. 37. Any of the architectures described belowcan be selected for use depending on the hardware and softwarepartitioning of the system.

FIG. 35 is a block diagram of hybrid position estimation using rangemeasurements from various systems, under an embodiment. The rangemeasurements (along with associated range quality metrics) are used fromGNSS and other positioning systems and combined in a single optimalposition solution by a hybrid position engine. This architecture is themost optimal in terms of using the available data to get the bestposition estimate out of them.

FIG. 36 is a block diagram of hybrid position estimation using positionestimates from various systems, under an embodiment. Independentposition estimates from different systems along with position qualityare used to choose the one with the best quality. This architecture isthe easiest to implement and integrate since the different positioningsystem are well isolated.

FIG. 37 is a block diagram of hybrid position estimation using acombination of range and position estimates from various systems, underan embodiment. For example, a position estimate from a WLAN positioningsystem can be compared with position estimate from range measurementsfrom GNSS and WAPS systems to arrive at the best solution.

Inertial Navigation Sensors (INS) such as accelerometers and gyros,magnetic sensors such as e-compass, pressure sensors such as altimeterscan be used to provide location aiding information (referred to as loosecoupling) or raw sensor measurements (referred to as tight coupling) tothe WAPS system for usage in tracking mode.

An accelerometer can be used in the receiver of an embodiment todetermine a frequency for updating the position reporting to the server.A combination of sequence of position solutions and accelerometermeasurements can be used to detect static position, constant velocityand/or other movement. This movement data or information can then beused to determine the frequency of the updates such that, for example,when there is non-uniform motion the frequency of updates can be set toa relatively high frequency, and when the receiver is at a constantvelocity or stationary for a pre-determined period of time the frequencyof the updates can be reduced to save power.

The sensor or position measurements can be combined into a positionsolution in a position filter (such as a Kalman filter). Two types oftight coupling architectures, where the sensor measurements are combinedwith GNSS and WAPS measurements in the WAPS hybrid position engine, areillustrated in FIG. 38 and FIG. 39. FIG. 38 is a flow diagram fordetermining a hybrid position solution in which position/velocityestimates from the WAPS/GNSS systems are fed back to help calibrate thedrifting bias of the sensors at times when the quality of the GNSS/WAPSposition and/or velocity estimates are good, under an embodiment. Thisarchitecture simplifies the algorithm formulation by partitioning thesensor calibration and position calculation parts of the algorithm.However, the drawback of this method is the complexity in deciding whenare the good times to re-calibrate the sensors using WAPS/GNSSestimates.

FIG. 39 is a flow diagram for determining a hybrid position solution inwhich sensor parameters (such as bias, scale and drift) are estimated aspart of the position/velocity computation in the GNSS and/or WAPS unitswithout need for explicit feedback, under an embodiment. For example,the sensor parameters can be included as part of the state vector of theKalman filter used for tracking the position/velocity of the receiver.This architecture provides an optimal solution in that the informationis used in one combined filter to update both position and sensorparameters.

Loose coupling is illustrated in FIG. 40 and FIG. 41 where a selectionunit selects between position estimate from the GNSS engine and the WAPSengine. Note that the selection unit may be part of the WAPS or GNSSposition units. FIG. 40 is a flow diagram for determining a hybridposition solution in which sensor calibration is separated from theindividual position computation units, under an embodiment. FIG. 41 is aflow diagram for determining a hybrid position solution in which thesensor parameter estimation is done as part of the state of theindividual position computation units, under an embodiment.

The loose coupling methods are generally worse than the tight couplingmethods since a selection uses information only from one system. Amongstloose coupling or tight coupling methods, the method that uses theranges along with raw sensor measurements to determine position andsensor parameters in one optimal filter are better than when sensorparameters and position are computed separately. As a result, thepreferred method from a performance perspective is the tight couplingsystem with implicit sensor parameter estimation. However, depending onthe hardware/software platform partitioning, one or more of thesemethods may be easily implemented and may be selected for that reason.

Information can also be exchanged between the WAPS system and othertransceiver systems on the same platform (such as cell-phone, laptop,PND). The transceiver systems can be, for example, Bluetoothtransceiver, WLAN transceiver, FM receiver/transmitter, digital oranalog TV system, MediaFLO, satellite communication system such as XMradio/Iridium, Cellular modem transceivers such as GSM/UMTS/cdma20001×/EVDO or WiMax). FIG. 42 shows the exchange of information between theWAPS and other systems, under an embodiment. The exchange of informationbetween systems can improve the performance of either system. Since theWAPS system time is aligned to GPS time, the WAPS system can providegood quality timing and frequency estimates to any other system. Timeand frequency estimates into the WAPS system can reduce the WAPSacquisition search space in code and frequency. In addition, the WAPSsystem can provide location information to the other transceiversystems. Similarly, if the other system has location information(partial position e.g., Altitude or 2-D position, or full position e.g.,3-D position or raw range/pseudo-range/range-difference) available, thatlocation information can be provided with or without a location qualitymetric to the WAPS system. The range/pseudo-range data should beprovided along with the location of transmitter (or other means tocompute the range from the transmitter location to any receiverlocation) to enable usage of this range information in a hybridsolution. The range difference corresponding to two transmitters shouldbe provided along with location of the two transmitters. The WAPS systemwill use the information to aid its position solution. Alternatively,location information can be provided in the form of ranges (orpseudo-ranges) from known transmitter locations to the receiver device.These ranges (or pseudo-ranges) would be combined with WAPS ranges bythe positioning algorithm to compute a hybrid position.

Examples of specific systems and information that can be exchangedbetween them are shown in FIG. 43, FIG. 44, and FIG. 45.

FIG. 43 is a block diagram showing exchange of location, frequency andtime estimates between FM receiver and WAPS receiver, under anembodiment. The location estimates from WAPS system can be provided toan FM Receiver. This location estimate may then be used, for example, toautomatically determine active FM radio stations in the local region.The FM signal may include a RDS—Radio Data Service) transmission aswell. If the location of the FM station is included in the RDS/RBDSdata-stream (for example, the Location and Navigation (LN) feature thatprovide data about the transmitter site, giving city and state name andprovide DGPS navigation data) then this information can be used toprovide location aiding to the WAPS Receiver. The frequency estimatefrom the WAPS system can be easily used to reduce the FM Receiver tuningtime for a particular station. In the other direction, the frequencyquality of the estimate in the FM Receiver is based on the FM radiostation transmit quality. The time estimate in the WAPS system is basedon GPS time and time can be transferred to the FM Receiver to aid timingalignment. Clock Time (CT) feature on RDS/RBDS transmissions may be usedto determine timing relative to the RDS data stream and can betransferred to the WAPS receiver.

FIG. 44 is a block diagram showing exchange of location, time andfrequency estimates between WLAN/BT transceiver and WAPS Receiver, underan embodiment. In general, these WLAN/BT transceivers do not have anaccurate frequency estimate and as a result the frequency estimateswould be quite coarse, so the transfer of such an estimate from WLAN/BTtransceiver to WAPS receiver may have limited value. In the reversedirection, a WAPS frequency estimate can reduce the time taken forfrequency acquisition on the WLAN system. The timing information that isextracted, for example, from the timestamp on the wireless LAN AP(Access Point) beacons can be transferred to the WAPS system to aid WAPSacquisition. Note that some reference of the WLAN timing relative to GPStime is needed to make this useful for the WAPS system. Similarly, ifthe WLAN/BT system has a location estimate (partial position e.g.,Altitude or 2-D position, or full position e.g., 3-D position or rawrange/pseudo-range) available, that location information can be providedwith or without a location quality metric to the WAPS system. The WLANposition estimate could simply be the geo-location of the serving AP orother “audible” APs in the vicinity. The WLAN position estimate couldalso be partial, for example, the altitude estimate based on the floorof the AP in question. The WLAN location information can also be a rangeestimate to a known transmitter AP location (for example, the WLANsystem may use Round Trip Time measurements to determine range estimate)or a range difference estimate between two transmit APs.

FIG. 45 is a block diagram showing exchange of location, time andfrequency estimates between cellular transceiver and WAPS receiver,under an embodiment. Location estimates (partial, complete or rawranges/range-differences) from cellular systems (such as from TDOA, AFLTor other similar cellular signal FL or RL based positioning method) canbe provided to the WAPS system which will use these measurements toobtain a better position estimate. Frequency estimates from thefrequency tracking loops of the cellular modem can be provided to theWAPS system to reduce the frequency search space and thus improve WAPSacquisition time (i.e. TTFF). Time estimates from the cellular systemcan also be provided to the WAPS system to reduce the code search spaceor to aid bit and frame alignment. For example, systems that aresynchronized to GPS time such as cdma2000/1×EVDO can provide fine timeestimates for the WAPS system whereas asynchronous (transmissions notsynchronized finely to time scale such as GPS) cellular systems such asGSM/GPRS/EGPRS/UMTS may provide coarse time estimates.

Since the WAPS system time is aligned to GPS time, the WAPS system canprovide good quality timing and frequency estimates to any other systemeven if not on the same platform. For example, the WAPS system can beused to provide timing information to a pico/femto-cell BTS through aperiodic hardware signal such as a pps (pulse-per-sec) aligned with GPSsecond-boundaries or a single pulse signal with an associated GPS time.

As described above, the spectrum used by the WAPS system of anembodiment can include licensed or unlicensed bands or frequencies.Alternatively, the WAPS system can use the “White Space” spectrum. Thewhite space spectrum is defined as any spectrum that the WAPS systemssenses or determines to be free in a local area (not limited to TV WhiteSpace) and transmits location beacons in that spectrum. The transmittersof an embodiment can use spectrum-sensing technology to detect unusedspectrum and/or communicate geo-location (can be readily obtained fromthe GPS timing receiver) to a centralized database that coordinates thespectrum. The receivers can include spectrum-sensing technology tolisten to these beacons, or in another embodiment, may be notified ofthe frequency to which to tune using the communication medium. The WAPSsystem can adapt to dynamic white space availability or allocation (incases where the transmitters are required to broadcast theirgeo-location to a centralized database which then allocates either thespectrum to transmit in and/or the time duration for which it needs totransmit). The WAPS system can continuously broadcast in this spectrumor can share the spectrum with other systems as controlled by acentralized coordination service for the spectrum. The chipping rate andthe data rate of the WAPS system components can be modified dynamicallyto suit the accuracy requirements and/or signal power and bandwidthavailability at any given time. The system parameters can be sensed bythe receiver or can be communicated to the receiver through thecommunication medium. The transmitters can form a local network or incases of spectrum availability in a wider geographical area, can form acontinuous network.

The transmitter of an embodiment can also coexist with other networks onthe same transmit system in a time-shared fashion. For example, the samespectrum can be used in a time-shared fashion between location and smartgrid applications. The transmitter is a broadcast transmitter using themaximum available power levels and can adjust its power levelsdynamically based on spectrum sensing or as requested by a centralizedcoordinating server. The receiver can employ spectrum sensing or can becommunicated by a communication medium (which can also be a white spacespectrum) of the system parameters and wake up times at that time.

Based on spectrum availability, the WAPS system of an embodiment can useone channel of the TV White space (6 MHz bandwidth) or, if multiplechannels are available, can use the multiple frequency bands for bettermultipath resolution. If adjacent channels are available, channelbonding (e.g., combining adjacent channels) can be used. The increasedbandwidth can be used for better multipath resolution, higher chippingrate for higher accuracy, etc. Alternatively, the available bandwidthcan be used under FDMA to help solve the near far problem and/ormultipath resolution.

White space transmission/reception of WAPS waveforms in two or morewhite-space bands can enable better and faster integer ambiguityresolution for WAPS carrier phase measurements. This will enablerelatively high accuracy (of the order of <1 wavelength) single pointpositioning using WAPS.

The whitespace bandwidth can also be used as a communication channel inthe WAPS (in cases where a reference receiver is used) between thereference receiver at surveyed location and the receiver whose positionis to be found.

When a WAPS system in the licensed band is available in a wide areanetwork, a White-Space based local network of towers can be used toaugment the location accuracies of the WAPS receiver. The receiver canbe designed to listen to both frequencies simultaneously or switchbetween the licensed band and white space band and tune to theappropriate frequencies.

The White-space bands can also be used to send assistance information tothe WAPS, GPS or AGPS systems for location aiding and other assistanceinformation like clock bias, satellite ephemeris etc.

In cases where multiple frequencies with wide separation are available,the WAPS system can be designed to take advantage of the diversity infrequencies to provide better multipath performance.

Correlator Implementation

In any CDMA receiver (or a receiver that uses Pseudo Random codes as apart of the transmit bit stream), correlation of the received signalwith its PRN code is essential. The more parallel correlations that canbe done, the faster is the time to acquire the channel. A brute forceimplementation of a parallel complex correlator architecture for signalsthat use a maximal length sequence of length 1023, input signaloversampled by 2×, is shown in FIG. 46. The even and odd samplescorrespond to the 2× oversampled data. The shift registers get shiftedat the rate of the ‘clk’. The PRN generator generates the reference PRNand gets shifted at the rate of clk/2. The correlation sum at each cycleis calculated using the equation corrsum[n]=Σ_(k=0) ²⁰⁴⁵gcref[k]*x[k−n], where x[n] is the complex input, gcref[k] is the PRNreference waveform, and corrsum[n] is the complex output from thecorrelator. FIG. 46 shows one optimization where the even and oddsamples share the same multiplier and adder trees.

An implementation like the one shown above requires 2046*2*n-input bitsflip flops for the shift registers, 1023 of 1×n-input multiplier and anadder that sums the 1023 products. As an example, if the input bit widthwere 2-bit samples, then 1023 of 1×2 multipliers are required, and 1023of these multiplications would have to be summed in one clock cycle.This could be an onerous implementation in terms of area, timing andpower in hardware. In particular, in an FPGA implementation a bruteforce implementation of the multiplier and adder structure may beimpossible to implement given the limited resources.

An embodiment includes a novel approach to this implementation whichtakes advantage of the structures available in state of the art FPGAs.Modern FPGAs include several configurable logic blocks (CLBs) thatimplement logic and storage elements. The lookup tables that form anessential part of the CLBs can also be reprogrammed as shift registerswith a serial shift in, but have parallel random access to the storageelements. This implementation can also be used in an ASIC implementationas an efficient approach to computing the correlation and as an easymigration path from FPGAs (used to prototyping) to ASICs (for massproduction volumes).

Turning to shift register implementation, particular FPGAs have shiftregister primitives which are mapped onto the CLBs. Some FPGAs have a16-bit shift register while some have a 32-bit shift register mapping.FIG. 47 shows a 32-bit shift register implementation derived from two16-bit shift register primitives with parallel random access readcapabilities. In this example implementation a 16-bit shift registergroup primitive is used to build a 32-bit shift register. 32 of such32-bit shift registers are strung in series to form the 1024-bit shiftregister. The shift operations occur at ‘clk’ rate, and the readoutoperations occur at 32 times the clock rate, as shown in FIG. 48.

The adder tree can also be complex to implement a 1023×n-bit adder. Inthe case of a particular FPGA, a 48-bit DSP slice is available which canbe used as 1023×n-bit sequential adder. The hardware structure for thisimplementation is shown in FIG. 49. The 32 values from the 32 groups ofshift registers are split into 4 groups of 8 additions. In this example,a 2-bit input is used. Each 8-number adder produces a 10-bit outputwhich is then aligned in a 12-bit group in the 48-bit adder. Room isallowed for the growth of the sum. After 32 cycles, the 1024 bit sum isobtained by adding the 4 groups of the 12-bit adders into one 14-bitsum.

Encryption and Security

The overhead information in the system of an embodiment can be encryptedusing an encryption algorithm. This allows users to use the system andbe billed for usage of the system and provide a means to controlinformation security. Keys can be applied to decrypt the signal. Thekeys can be obtained using a PC, wireless network, hardware dongle orcan be burnt into the non volatile memory of the device in a way that itis inaccessible by any unintended sources.

The encryption of an embodiment provides both data security andauthentication. The key components that are secured using encryption arethe transmitters, the receivers and the server communication.Transmitter Authentication includes unambiguously identifyingtransmitters so that malicious transmitters can be rejected. ReceiverAuthentication is such that only authentic receivers should be able toutilize the transmitted information. Receiver Authorization is such thatonly receivers that are authorized (authentic receiver) should bepermitted to operate. Server Communication is encrypted such thatcommunication between the receivers and the server and between thetransmitters and the server has to be secure. User data protection isalso encrypted because location tracking user databases requireprotection from unauthorized access.

Encryption methods of an embodiment can be broadly classified into twotypes: symmetric key cryptography and asymmetric key cryptography.Symmetric Key encryption provides both authentication and encryption,whereas asymmetric key encryption provides authentication of the privatekey owner, since the public key is available to anyone. Symmetric Keyencryption of data is an order of magnitude faster given similarresources. 3DES and AES are examples of symmetric key cryptography. Acombination of both methods is used as part of the encryptionarchitecture of an embodiment.

Over-the-air (OTA) broadcast messages can comprise general broadcastmessages or system messages. General broadcast messages contain dataspecific to each transmitter such as location information, transmittertiming counts and other pertinent information that assist a receiver indetermining its location. System messages are used to configureencryption keys, enable/disable receivers or for targeted one-wayprivate information exchange to a specific set of receivers.

The general format of a message of an embodiment includes: Message type(parity/ECC protected); Encrypted Message; and Encrypted Message ECC.The ECC for the encrypted message is computed after the message isencrypted.

The OTA broadcast comprises frames that are transmitted periodically,possibly every second. Depending on the channel data rate, a messagecould be split up (segmented) over multiple frames. Each frame comprisesa frame type and frame data. Frame type (parity protected) indicateswhether this is the first frame of a message or if it is a continuingframe; it can also indicate a low level format frame that may be usedfor other purposes. Frame Data is essentially a segmented Message or alow level data frame.

OTA system messages can be encrypted either by the session key or by thetransmitter's private key depending upon the system message type. OTAgeneral broadcast messages are encrypted using a symmetric key algorithmwith a session key that both the transmitter and receiver havenegotiated as described herein. This provides mutual authenticationi.e., transmitters can be authenticated by receivers and onlyauthenticated receivers can decode the OTA broadcast. The session key isknown to all transmitters and receivers and it is changed periodically.Key change messages are encrypted using the past few session keys,allowing receivers that were not active at a certain time period to syncup to the current session key.

OTA broadcasts also include periodic system messages encrypted by thetransmitter's private key. The receivers can unambiguously identify theauthenticity of the transmitter by using the associated public key. Inthe event the session key is compromised, this mechanism ensures thatunauthorized transmitters cannot be implemented.

FIG. 50 is a block diagram of session key setup, under an embodiment.Each receiver is equipped with a unique device ID and a device specifickey. FIG. 51 is a flow diagram for encryption, under an embodiment. TheWAPS System data servers maintain a database of the device ID/devicespecific key pairing. Receiver initialization between a receiver and theWAPS data servers is facilitated using a data connection(GPRS/USB/Modem, etc.) specific to the receiver type. This connection isencrypted using the device specific key after the device identifiesitself with the device ID. During this initialization, the currentsession key, the transmitter public key and licensing terms (i.e.,duration the receiver is authorized) are exchanged. Receiverinitialization can be performed when the receiver has lost the currentsession key (initial power up) or if its session key is out of sync(extended power off). The session key is periodically updated, and thenew key used for the updating is encrypted using the previous N keys.

The OTA data rate may be inadequate for being the sole mechanism toauthorize receivers. However, the system message protocol of anembodiment supports device ID specific and device ID range-basedreceiver authorization.

A compromised session key requires all receivers to re-initialize.Therefore the session key storage should be tamper-proof in the device.Session key stored outside the device crypto boundary (i.e., attachedstorage of any kind) will be encrypted using the device's secure key.

A compromised session key cannot be used to masquerade a transmitterbecause the transmitter periodically transmits authenticationinformation using its private key. Therefore, the transmitter's privatekey should never be compromised.

In an alternative embodiment, shown in FIG. 52, the keys can be directlydelivered to the receiver over the communication link from the WAPSserver or can be routed through a third party application or serviceprovider. The keys can have a certain validity period. The keys can bemade available on a per-application basis or a per device basis based ona contractual agreement with the customer. Every time a position requestis made either by an application on the receiver or by an application onthe network, the keys are checked for validity before retrieving theposition or parameters to compute position from the WAPS engine. The keyand information exchange to a WAPS server can happen using proprietaryprotocols or through standard protocols such as OMA SUPL.

The security architecture of the system can be implemented ascombination of architectures shown in FIG. 50 and FIG. 52.

Parameter sensors can be integrated into receivers of the WAPS system totime tag and/or location tag the measurements from the sensors. Theparameter sensors can include, but are not limited to, temperaturesensors, humidity sensors, weight sensors, and sensors for scanner typesto name a few. For example, an X-ray detector can be used to determineif a tracked receiver, or device including a tracked receiver, passesthrough an X-ray machine. The time of the X-ray event and location ofthe X-ray machine can be tagged by the detector. In addition, otherparameter sensors can be integrated into the WAPS system to both timetag and location tag measurements from the sensors.

Users can be billed for the system on a per use, per application on thedevice, hourly, daily, weekly, monthly and annual basis for anindividual or asset.

The location and height of the receiver unit can be sent to anyapplication on the terminal or to the network server using acommunication protocol. Alternatively, the raw range measurement can besent to the network through a communication protocol. The communicationprotocol can be a standard serial or other digital interface to theapplication on the terminal or through a standard or proprietarywireless protocol to the server. Possible methods of coupling orconnecting to a server through a standard protocol includes the use ofSMS messaging to another phone connected to the server or,alternatively, through a wireless data service to a web server. Theinformation sent includes one or more of latitude/longitude, height (ifavailable), and timestamp. The application on the server or the terminalunit can initiate a position fix. The location of the user can becommunicated directly from the server or by the application on theserver.

The WAPS standalone system independent of a GPS receiver can be used fordetermining the location of a device. The WAPS system by itself orintegrated WAPS and GPS and/or other positioning system can beimplemented to co-exist with media storage cards (such as SD cards) onthe media cards. The WAPS system by itself or integrated WAPS and GPSsystem and/or other positioning systems can be implemented to co-existon a cellular phone Subscriber Identity Module (SIM) card so that theSIM cards can be tracked.

Precise Positioning with Carrier Phase

One method to augment the WAPS system performance to further improveaccuracy (up to <1 m) is to implement a carrier phase positioning systemas described below. The beacons are set up as usual WAPS transmitters.For this method, it may be desirable (but not essential) to not use TDMAslotting to facilitate easy continuous phase tracking. When TDMA is notused, the near-far problem can be overcome through interferencecancellation and increased dynamic range in the receiver. The WAPSreceiver to support such a method is capable of measuring andtime-stamping code and carrier phase in a continuous manner for allvisible satellites. In addition, there is a reference receiver at aknown surveyed location that can also make similar measurements of codeand carrier phase in a continuous manner. The measurements from the WAPSreceiver and the reference receiver may be combined to compute aposition either on the device or on the server. The configuration ofsuch a system would be identical to a differential WAPS system.

Carrier phase measurement is more accurate than code phase measurementbut contains unknown integer number of carrier phase cycles calledinteger ambiguity. However there are ways to find integer ambiguitiescalled ambiguity resolution. One method will be considered here thatuses extension of local minima search algorithm to iteratively solve foruser receiver position and uses measurements at multiple epochs forimproved accuracy.

Consider carrier phase measurement at user receiver at a single epochfirst as follows.

ϕ_(u) ^((k))=λ⁻¹ ·r _(u) ^((k)) +N _(u) ^((k))+ƒ·(dt _(u) −dt^((k)))+ε_(u) ^((k))  (1)

where ϕ, λ, ƒ and N are carrier phase, wavelength, frequency and integercycles respectively, dt is clock bias, r is range, ε is measurementerror and subscript u represents user receiver k represents transmitternumber.Range is given in terms of user and transmitter positions p_(u) andp^((k)) as

r _(u) ^((k)) =∥p _(u) −p ^((k))∥=√{square root over ((p _(ux) −p _(x)^((k)))²+(p _(uy) −p _(y) ^((k)))²+(p _(uz) −p _(z) ^((k)))²)}  (2)

To eliminate error in the knowledge of transmitter clock bias consideranother receiver at known position (called reference receiver) withcorresponding carrier phase equation

ϕ_(r) ^((k))=λ⁻¹ ·r _(r) ^((k)) +N _(r) ^((k))+ƒ·(dt _(r) −dt^((k)))+ε_(r) ^((k))  (3)

where subscript r stands for reference receiver and subtract (2) from(1) to get

ϕ_(u) ^((k))−ϕ_(r) ^((k))=λ⁻¹·(r _(u) ^((k)) −r _(r) ^((k)))+(N _(u)^((k)) −N _(r) ^((k)))+ƒ·(dt _(u) −dt _(r))+(ε_(u) ^((k))−ε_(r)^((k)))  (4)

which is written as

ϕ_(ur) ^((k))=λ⁻¹ ·r _(ur) ^((k)) +N _(ur) ^((k)) +ƒ·dt _(ur)+ε_(ur)^((k))  (5)

where (●)_(ur)=(●)_(u)−(●)_(r).Since dt_(u)r is not of interest it can be eliminated by differencing(5) for different values of index (k) to get so called double differenceobservable equation

ϕ_(ur) ^((kl))=λ⁻¹ ·r _(ur) ^((kl)) +N _(ur) ^((kl))+ε_(ur) ^((kl))  (6)

where (●)_(ur) ^((kl))=(●)_(ur) ^((k))−(●)_(ur) ^((l)).Equation (6) then is an equation in the unknown user position p_(u)through r_(ur) ^((kl)) as

r _(ur) ^((kl))=(r _(u) ^((k)) −r _(r) ^((k)))−(r _(u) ^((l)) −r _(r)^((l)))=∥p _(u) −p ^((k)) ∥−∥p _(u) −p ^((l))∥−γ^((kl))  (7)

where

γ^((kl)) =∥p _(r) −p ^((k)) ∥−∥p _(r) −p ^((l))∥  (8)

Typically transmitter l used in double differencing is one of thetransmitters and labeling it as 1 for convenience leads to equation inthe matrix form as

$\begin{matrix}{\begin{bmatrix}\varphi_{ur}^{(21)} \\\varphi_{ur}^{(31)} \\\vdots \\\varphi_{ur}^{(n)}\end{bmatrix} = {{\lambda^{- 1} \cdot \begin{bmatrix}{{{p_{u} - p^{(2)}}} - {{p_{u} - p^{(1)}}} - \gamma^{(21)}} \\{{{p_{u} - p^{(3)}}} - {{p_{u} - p^{(1)}}} - \gamma^{(31)}} \\\vdots \\{{{p_{u} - p^{(n)}}} - {{p_{u} - p^{(1)}}} - \gamma^{({n\; 1})}}\end{bmatrix}} + \begin{bmatrix}N_{ur}^{(21)} \\N_{ur}^{(31)} \\\vdots \\N_{ur}^{({n\; 1})}\end{bmatrix} + {\begin{bmatrix}ɛ_{ur}^{(21)} \\ɛ_{ur}^{(31)} \\\vdots \\ɛ_{ur}^{({n\; 1})}\end{bmatrix}\mspace{14mu} {or}}}} & (9) \\{\mspace{79mu} {\varphi = {{\lambda^{- 1} \cdot {f\left( p_{u} \right)}} + N + ɛ}}} & (10)\end{matrix}$

Equation (10) is a nonlinear equation in unknown user position p_(u).Local minima search algorithm works on linear equations and so (10) islinearized and solved iteratively as follows. Let at iteration m,approximation to p_(u) is p_(u) ^(m) where

$\begin{matrix}{{p_{u} = {p_{u}^{m} + {\Delta \; p_{u}}}}{and}} & (11) \\{{{f\left( p_{u} \right)} = {{f\left( {p_{u}^{m} + {\Delta \; p_{u}}} \right)} \approx {{f\left( p_{u}^{m} \right)} + {\frac{\partial f}{\partial p_{u}}{\left( p_{u}^{m} \right) \cdot \Delta}\; p_{u}}}}}{where}} & (12) \\{{{\frac{\partial f}{\partial p_{u}}\left( p_{u} \right)} = \begin{bmatrix}{l^{(2)} - l^{(1)}} \\{l^{(3)} - l^{(1)}} \\\vdots \\{l^{(n)} - l^{(1)}}\end{bmatrix}},} & (13)\end{matrix}$

where l^((k)) is line-of-sight row vector

$l^{(k)} = \frac{p_{u} - p^{(k)}}{{p_{u} - p^{(k)}}}$

Then equation (10) is written as,

$\begin{matrix}{{y = {{G \cdot x \cdot {+ N}} + ɛ}}{{{{where}\mspace{14mu} y} = {\varphi - {\lambda^{- 1} \cdot {f\left( p_{u}^{m} \right)}}}},{G = {{\lambda^{- 1} \cdot \frac{\partial f}{\partial p_{u}}}\left( p_{u}^{m} \right)}},{and}}{x = {\Delta \; p_{u}}}} & (13)\end{matrix}$

Equation (13) is linear in x=Δp_(u) and is solved for Δp_(u) using localminima search algorithm given below. Using so obtained solution ofΔp_(u) equation (11) is used to get p_(u) at iteration m and then soobtained p_(u) is used as p_(u) ^(m+1) at the next iteration (m+1). Theiterations are continued till Δp_(u) becomes small enough to decideconvergence. At the beginning of iterations p_(u) ⁰ can be taken fromcode phase based solution.

Now consider solving equation (13). Let Q_(dd) be covariance matrix ofdouble difference carrier phase error vector. It is obtained as follows.Variance of error in single difference observable ϕ_(ur) ^((k))=ϕ_(u)^((k))−ϕ_(r) ^((k)) is Q_(u)+Q_(r) where Q_(u) and Q_(r) are respectivecarrier phase error variances which are assumed to be independent oftransmitter k. Variance of ϕ_(ur) ^((k1))=ϕ_(ur) ^((k))−ϕ_(ur) ⁽¹⁾ is2·(Q_(u)+Q_(r)) and cross-variance between ϕ_(ur) ^((j1))=ϕ_(ur)^((j))−ϕ_(ur) ⁽¹⁾ and ϕ_(ur) ^((k1))=ϕ_(ur) ^((k))−ϕ_(ur) ⁽¹⁾, j≠k isQ_(u)+Q_(r) which is variance of the common term ϕ_(ur) ⁽¹⁾. So,

$\begin{matrix}{Q_{dd} = {\left( {Q_{u} + Q_{r}} \right) \cdot \begin{bmatrix}2 & 1 & \ldots & 1 \\1 & 2 & \ldots & 1 \\\vdots & \vdots & \ddots & \vdots \\1 & 1 & \ldots & 2\end{bmatrix}}} & (14)\end{matrix}$

Weighted least squares solution of (13) is:

{circumflex over (x)}=G ^(L)·(y−N) where G ^(L) is left inverse of G, G^(L)=(G ^(T) ·Q _(dd) ⁻¹ ·G)⁻¹ ·G ^(T) ·Q _(dd) ⁻¹  (15)

Vector of residuals is then

(Y−N)−G·{circumflex over (x)}=(y−N)−G·G ^(L)(y−N)=(I−G·G^(L))(y−N)=S(y−N)  (16)

which is a function of N and local minima search tries to minimizeweighted norm square of residuals with respect to N as

min c(N)=(y−N)^(T) ·W·(y−N), where W=S ^(T) ·Q _(dd) ⁻¹ ·S and S=I−G·G^(L)  (17)

To solve (17) consider solving

W·N≈W·y  (18)

under the constraint that N is integer. Then W·(y−N)≈0 and(y−N)^(T)·W^(T)·W·(y−N)=(y−N)^(T)·W·(y−N)=c(N)≈0 because W is idempotent(W^(T)=W and W·W=W). Thus search for N is limited to those N whichsatisfy (18).

Once N is solved for estimate of x=Δp_(u) is obtained from equation(15).

Matrices G and G^(L), of dimensions (n−1)×3 and 3×(n−1) respectivelyhave rank 3 each since (n−1)>3 and so (n−1)×(n−1) matrices S and W willfall short from full rank of (n−1) by 3.

Using QR decomposition of W (LU decomposition could also be used) onequation (18),

R·N=Q ^(T) ·W·y  (19)

where Q is ortho-normal matrix (Q⁻¹=Q^(T)) and R is upper triangular sothat

$\begin{matrix}{{\begin{bmatrix}R_{11} & R_{12} \\0 & 0\end{bmatrix} \cdot \begin{bmatrix}N_{1} \\N_{2}\end{bmatrix}} = \begin{bmatrix}\left( {Q^{T} \cdot W \cdot y} \right)_{11} \\{\approx 0}\end{bmatrix}} & (20)\end{matrix}$

and then

N ₁=round{R ₁₁ ⁻¹·((Q ^(T) ·W·y)₁₁ −R ₁₂ ·N ₂)}  (21)

Thus solution of

$N = \begin{bmatrix}N_{1} \\N_{2}\end{bmatrix}$

is obtained by searching for N₂ in 3 dimensional box with integervalues, obtaining N₁ from (21), and picking that N which minimizes c(N)in (17). Search for N₂ is centered on the value of N₂ from the previousiteration. At the zero-th iteration N₂ latter part of N which isobtained as fractional part of λ⁻¹·ƒ(p_(u) ⁰); p_(u) ⁰ being the codephase based solution. The size of the 3 dimensional search box dependson the uncertainty in the code phase based solution. This box can bedivided into smaller sub-boxes and center of each smaller size sub-boxcan be tried as initial p_(u) ⁰.

The above method used a single epoch (instant) of measurement todetermine position. The description below explains an extension to thesingle epoch method. Multiple epoch measurements are taken close enoughin time wherein user receiver movement is negligible. Further, integerambiguities of the initial epoch remain the same for subsequent epochsso that no new unknown integer ambiguities are introduced at subsequentepochs. Multiple epoch measurements do not give independent equationsbecause transmitter locations are fixed (unlike in the GNSS case wheremotion of satellite transmitters change line-of-sight and thus giveindependent equations). So multiple epoch measurements do not help insolving for integer ambiguities as float ambiguities (unlike in GNSScase when number of independent equations become greater than number ofunknown ambiguities plus three position coordinates). However, multipleepoch measurements allow more carrier phase measurement errors and stillallow successful ambiguity resolution. In the multiple epoch caseequation (13) becomes

$\begin{matrix}{y = {\begin{bmatrix}y_{1} \\y_{2} \\\vdots \\y_{m}\end{bmatrix} = {{\begin{bmatrix}G \\G \\\vdots \\G\end{bmatrix} \cdot x} + \begin{bmatrix}N \\N \\\vdots \\N\end{bmatrix} + \begin{bmatrix}ɛ_{1} \\ɛ_{2} \\\vdots \\ɛ_{m}\end{bmatrix}}}} & (22)\end{matrix}$

Following development for single epoch case as above equation, theproblem reduces to problem of finding N such that

$\begin{matrix}{{{{\min \; {c(N)}} = {\left( {y - \begin{bmatrix}N \\N \\\vdots \\N\end{bmatrix}} \right)^{T} \cdot \overset{\_}{W} \cdot \left( {y - \begin{bmatrix}N \\N \\\vdots \\N\end{bmatrix}} \right)}},{{{where}\mspace{14mu} \overset{\_}{W}} = {{\overset{\_}{S}}^{T} \cdot {\overset{\_}{Q}}_{dd}^{- 1} \cdot \overset{\_}{S}}},{\overset{\_}{S} = {I - {\overset{\_}{G} \cdot {\overset{\_}{G}}^{L}}}},{{\overset{\_}{G}}^{L} = {\left( {{\overset{\_}{G}}^{T} \cdot {\overset{\_}{Q}}_{dd}^{{- 1} \cdot} \cdot \overset{\_}{G}} \right)^{- 1} \cdot {\overset{\_}{G}}^{T} \cdot {\overset{\_}{Q}}_{dd}^{- 1}}}}{\overset{\_}{G} = {{\begin{bmatrix}G \\G \\\vdots \\G\end{bmatrix}{\overset{\_}{Q}}_{dd}^{- 1}} = \begin{bmatrix}Q_{dd}^{- 1} & 0 & \ldots & 0 \\0 & Q_{dd}^{- 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & Q_{dd}^{- 1}\end{bmatrix}}}} & (23)\end{matrix}$

And to solve (23) for N consider solving

$\begin{matrix}{{{\overset{\_}{W} \cdot \overset{\_}{I} \cdot N} \approx {\overset{\_}{W} \cdot y}}{{{where}\mspace{14mu} \overset{\_}{I}} = \begin{bmatrix}I \\I \\\vdots \\I\end{bmatrix}}} & \square\end{matrix}$

using QR decomposition of W·Ī (LU decomposition could also be used) andfollowing equations of (19) to (21) as above. Again, once N is solvedfor estimate of x=Δp_(u) is obtained from equation (15). If thisestimate of x=Δp_(u) is small then iterations in equation (11) arestopped to obtain user position p_(u). Typically if each component of xis less than 1e-6 in magnitude then convergence is declared anditerations are stopped.

The next step is to verify whether the converged user position p_(u) isthe right one. This is done based on residuals obtained from (10) asmod(ϕ−λ⁻¹·ƒ(p_(u))−N, λ). If maximum of absolute values of residuals foreach epoch is less than κ·√{square root over (Q_(r))} then convergedsolution is accepted as a solution otherwise the search is continued byselecting a new sub-box. Typically scale factor κ in the verificationtest can be chosen to be 5. Once the solution is verified, thedifferential WAPS system described above can achieve accuracy close toor better than 1 m.

This differential WAPS carrier phase system may be overlaid on top ofthe traditional WAPS system through the addition of reference receiversor can be standalone. The differential WAPS carrier phase system can beused to deliver high accuracy positioning in certain localized targetareas (such as malls, warehouses etc.).

In W-CDMA systems, two receive chains are used to improve the receivediversity. When WAPS co-exists with W-CDMA, one of the receive chainscan be used temporarily for receiving and processing the WAPS signal. Incertain cases of W-CDMA and CDMA architectures, the entire receive chaincan be reused to receive WAPS signal by tuning the receiver to WAPS bandand processing the WAPS signal while temporarily suspending theprocessing of the W-CDMA/CDMA signals. In certain other embodimentswhere the GSM receive chain is multiplexed with the W-CDMA receivechain, the receiver can be further time-shared to be used for WAPSreception.

Once it is determined which signals are used from which towers forposition determination in WAPS or any other TDMA system, in order tosave power, most of the receiver of an embodiment is turned off duringthe slots at which either signal is not detected and/or signals fromtowers that radiate in those slots are not used for positiondetermination. In case of detection of motion or change in position orchange in signal conditions, then the receiver of an embodiment isturned ON for all the slots to determine which slots can be used fornext set of position calculations.

Embodiments described herein include a method for transmitting positionlocation signals from a plurality of transmitters. The method comprisesselecting a set of digital pseudorandom sequences. Magnitudes of across-correlation function between any two sequences of the set ofdigital pseudorandom sequences are below a specified threshold. Themethod comprises selecting from the set of digital pseudorandomsequences a subset of digital pseudorandom sequences. The magnitudes ofan autocorrelation function of each member of the subset of digitalpseudorandom sequences, within a specified region adjacent to a peak ofthe autocorrelation function, are at least one of equal to and less thana prescribed value. The method comprises transmitting from eachtransmitter of the plurality of transmitters a positioning signal. Atleast a first portion of each positioning signal is modulated inaccordance with at least one member of the subset of digitalpseudorandom sequences. At least two transmitters of the plurality oftransmitters modulate the first portion of respective positioningsignals in accordance with different members of the subset of digitalpseudorandom sequences.

Embodiments described herein include a method for transmitting positionlocation signals from a plurality of transmitters, comprising: selectinga set of digital pseudorandom sequences, wherein magnitudes of across-correlation function between any two sequences of the set ofdigital pseudorandom sequences are below a specified threshold;selecting from the set of digital pseudorandom sequences a subset ofdigital pseudorandom sequences, wherein the magnitudes of anautocorrelation function of each member of the subset of digitalpseudorandom sequences, within a specified region adjacent to a peak ofthe autocorrelation function, are at least one of equal to and less thana prescribed value; and transmitting from each transmitter of theplurality of transmitters a positioning signal, wherein at least a firstportion of each positioning signal is modulated in accordance with atleast one member of the subset of digital pseudorandom sequences,wherein at least two transmitters of the plurality of transmittersmodulate the first portion of respective positioning signals inaccordance with different members of the subset of digital pseudorandomsequences.

The set of digital pseudorandom sequences comprises a set of binarypseudorandom sequences. The set of binary pseudorandom sequences isselected from a set of Gold codes. The prescribed value is the peakvalue of the autocorrelation function divided by a non-repeating lengthof the digital pseudorandom sequences. The set of binary pseudorandomsequences is one of Kasami codes, Bent codes, and Gold-like codes.

At least one digital pseudorandom sequence of the set of digitalpseudorandom sequences has a truncated sequence length, wherein thetruncated sequence length is shorter than a standard sequence length. Atleast one digital pseudorandom sequence of the set of digitalpseudorandom sequences has an extended sequence length, wherein theextended sequence length is longer than a standard sequence length.

The method comprises transmitting from at least one of the plurality oftransmitters a positioning signal during a first period of time forwhich the first portion of the positioning signal is modulated with afirst member of the subset of digital pseudorandom sequences, whereinthe first member of the subset of digital pseudorandom sequences has afirst length, and transmitting the positioning signal during a secondperiod of time for which a second portion of the positioning signal ismodulated with a second member of the subset of digital pseudorandomsequences, wherein the second member of the subset of digitalpseudorandom sequences has a second length.

The first length and the second length are different.

The second portion of the positioning signal is further modulated inaccordance with a data sequence.

The set of digital pseudorandom sequences have an alphabet size greaterthan two (2).

The set of digital pseudorandom sequences is a set of quaternarysequences.

The alphabet size is a power of two (2).

The specified region adjacent to the peak of the autocorrelationfunction comprises at least ten (10) consecutive symbols immediatelyadjacent to the peak of the autocorrelation function.

Embodiments described herein include a transmitter in a positioningsystem comprising a plurality of transmitters. The transmitter comprisesa processor coupled to a memory. The processor is running at least oneapplication. The at least one application selects a set of digitalpseudorandom sequences, and magnitudes of a cross-correlation functionbetween any two sequences of the set of digital pseudorandom sequencesare below a specified threshold. The at least one application selectsfrom the set of digital pseudorandom sequences a subset of digitalpseudorandom sequences. The magnitudes of an autocorrelation function ofeach member of the subset of digital pseudorandom sequences, within aspecified region adjacent to a peak of the autocorrelation function, areat least one of equal to and less than a prescribed value. The at leastone application transmits a positioning signal, wherein at least a firstportion of the positioning signal is modulated in accordance with atleast one member of the subset of digital pseudorandom sequences. Thetransmitter modulates positioning signals in accordance with a member ofthe subset of digital pseudorandom sequences different than that used byat least one other transmitter in the plurality of transmitters.

Embodiments described herein include a transmitter in a positioningsystem comprising a plurality of transmitters, the transmittercomprising: a processor coupled to a memory, wherein the processor isrunning at least one application, wherein the at least one application,selects a set of digital pseudorandom sequences, wherein magnitudes of across-correlation function between any two sequences of the set ofdigital pseudorandom sequences are below a specified threshold; selectsfrom the set of digital pseudorandom sequences a subset of digitalpseudorandom sequences, wherein the magnitudes of an autocorrelationfunction of each member of the subset of digital pseudorandom sequences,within a specified region adjacent to a peak of the autocorrelationfunction, are at least one of equal to and less than a prescribed value;and transmits a positioning signal, wherein at least a first portion ofthe positioning signal is modulated in accordance with at least onemember of the subset of digital pseudorandom sequences, wherein thetransmitter modulates positioning signals in accordance with a member ofthe subset of digital pseudorandom sequences different than that used byat least one other transmitter in the plurality of transmitters.

The set of digital pseudorandom sequences comprises a set of binarypseudorandom sequences.

The set of binary pseudorandom sequences is selected from a set of Goldcodes.

The prescribed value is the peak value of the autocorrelation functiondivided by a non-repeating length of the digital pseudorandom sequences.

The set of binary pseudorandom sequences is one of Kasami codes, Bentcodes, and Gold-like codes.

At least one digital pseudorandom sequence of the set of digitalpseudorandom sequences has a truncated sequence length, wherein thetruncated sequence length is shorter than a standard sequence length.

At least one digital pseudorandom sequence of the set of digitalpseudorandom sequences has an extended sequence length, wherein theextended sequence length is longer than a standard sequence length.

The transmitter comprises transmitting the positioning signal during afirst period of time for which first portion of the positioning signalis modulated in accordance with a first member of the subset of digitalpseudorandom sequences, wherein the first member of the subset ofdigital pseudorandom sequences has a first length, and transmitting thepositioning signal during a second period of time for which a secondportion of the positioning signal is modulated with a second member ofthe subset of digital pseudorandom sequences, wherein the second memberof the subset of digital pseudorandom sequences has a second length.

The first length and the second length are different.

The set of digital pseudorandom sequences have an alphabet size greaterthan two (2).

The set of digital pseudorandom sequences is a set of quaternarysequences.

The alphabet size is a power of two (2).

The specified region adjacent to the peak of the autocorrelationfunction comprises at least ten (10) consecutive symbols immediatelyadjacent to the peak of the autocorrelation function.

The first portion of the positioning signal is modulated in accordancewith a member of the subset of digital pseudorandom sequences, and asecond portion of the positioning signal includes the positioning signalfurther modulated in accordance with a data sequence.

The plurality of transmitters is synchronized. The plurality oftransmitters transmits assistance data. The plurality of transmittersforms a CDMA network. Alternatively, the plurality of transmitters formsa TDMA network. A carrier signal of at least one transmitter is offsetin frequency from the carrier signal of at least one other transmitterof the plurality of transmitters.

The assistance data comprises at least one of system time at a risingedge of a pulse of a waveform, system time at a falling edge of a pulseof a waveform, geocode data of the plurality of transmitters, geocodedata of transmitters adjacent to each of the plurality of transmitters,index of a sequence used by at least one transmitter in proximity of theplurality of transmitters, clock timing corrections for at least onetransmitter, local atmospheric corrections, and indication of localenvironment.

Embodiments described herein include a receiver in a positioning system.The receiver comprises a processor coupled to a memory. The processor isrunning at least one application that acquires positioning signals froma plurality of transmitters and computes position information of thereceiver using the positioning signals. At least a first portion of afirst positioning signal is modulated in accordance with a member of asubset of digital pseudorandom sequences. At least a first portion of asecond positioning signal is modulated in accordance with a differentmember of the subset of digital pseudorandom sequences. Selection of thesubset of digital pseudorandom sequences comprises selecting a set ofdigital pseudorandom sequences such that magnitudes of across-correlation function between any two sequences of the set ofdigital pseudorandom sequences are below a specified threshold, andselecting the subset of digital pseudorandom sequences from the set ofdigital pseudorandom sequences. The magnitudes of an autocorrelationfunction of each member of the subset of digital pseudorandom sequences,within a specified region adjacent to the peak of the autocorrelationfunction, are at least one of equal to and less than a prescribed value.

Embodiments described herein include a receiver in a positioning system,comprising: a processor coupled to a memory, wherein the processor isrunning at least one application that acquires positioning signals froma plurality of transmitters and computes position information of thereceiver using the positioning signals, wherein at least a first portionof a first positioning signal is modulated in accordance with a memberof a subset of digital pseudorandom sequences, wherein at least a firstportion of a second positioning signal is modulated in accordance with adifferent member of the subset of digital pseudorandom sequences;wherein selection of the subset of digital pseudorandom sequencescomprises selecting a set of digital pseudorandom sequences such thatmagnitudes of a cross-correlation function between any two sequences ofthe set of digital pseudorandom sequences are below a specifiedthreshold, and selecting the subset of digital pseudorandom sequencesfrom the set of digital pseudorandom sequences, wherein the magnitudesof an autocorrelation function of each member of the subset of digitalpseudorandom sequences, within a specified region adjacent to the peakof the autocorrelation function, are at least one of equal to and lessthan a prescribed value.

The set of digital pseudorandom sequences comprises a set of binarypseudorandom sequences. The set of binary pseudorandom sequences isselected from a set of Gold codes. The prescribed value is the peakvalue of the autocorrelation function divided by a non-repeating lengthof the digital pseudorandom sequences. The set of binary pseudorandomsequences is one of Kasami codes, Bent codes, and Gold-like codes.

At least one digital pseudorandom sequence of the set of digitalpseudorandom sequences has a truncated sequence length, wherein thetruncated sequence length is shorter than a standard sequence length.Alternatively, at least one digital pseudorandom sequence of the set ofdigital pseudorandom sequences has an extended sequence length, whereinthe extended sequence length is longer than a standard sequence length.

A second portion of the first positioning signal is modulated inaccordance with a member of the subset of digital pseudorandomsequences.

The member of the subset of digital pseudorandom sequences used tomodulate the first portion has a first sequence length, and the memberof the subset of digital pseudorandom sequences used to modulate thesecond portion has a second sequence length, and the first sequencelength is different from the second sequence length.

The member of the subset of digital pseudorandom sequences used tomodulate the first portion is different from the member of the subset ofdigital pseudorandom sequences used to modulate the second portion.

The set of digital pseudorandom sequences have an alphabet size greaterthan two (2). The set of digital pseudorandom sequences is a set ofquaternary sequences. The alphabet size is a power of two (2).

The specified region adjacent to the peak of the autocorrelationfunction comprises at least ten (10) consecutive symbols immediatelyadjacent to the peak of the autocorrelation function.

A first portion of the positioning signal is modulated with a member ofthe subset of digital pseudorandom sequences, and a second portion ofthe positioning signal includes the positioning signal further modulatedin accordance with a data sequence.

The positioning signal includes data describing timing differencesbetween transmissions from different transmitters of the plurality oftransmitters.

Each of the positioning signals is initially synchronized to a timereference, and timing corrections corresponding to the synchronizationare provided to the receiver.

The receiver identifies multipath components of the positioning signalsusing high resolution earliest time of arrival estimates that include anestimated reference correlation function.

The receiver identifies multipath components of the positioning signalsusing high resolution earliest time of arrival estimates that include apartitioning of signal and noise subspaces.

The receiver identifies multipath components of the positioning signalsby generating a cross-correlation function by cross-correlating receivedsamples with a sequence transmitted from a transmitter, and extractingfrom the cross-correlation function a peak vector that includes a firstnumber of samples left of a peak of the cross-correlation function and asecond number of samples right of the peak.

The receiver identifies multipath components of the positioning signalsby generating a reference peak vector from a correlation functionmeasured in a channel environment that has low noise and at least one ofeasily separable multipath and no-multipath components, and improving asignal-to-noise ratio in the peak vector by coherently averaging acrossat least a plurality of pseudorandom code periods.

The receiver identifies multipath components of the positioning signalsby calculating a Fourier Transform of the peak vector, and generating afrequency domain estimate of a channel corresponding to the transmittedsequence using the Fourier Transform of a measured peak vector and theFourier Transform of the reference peak vector.

The receiver identifies multipath components of the positioning signalsby generating a reduced channel estimate vector from the frequencydomain estimate of the channel, defining an estimated covariance matrixof the reduced channel estimate vector, and performing singular valuedecomposition on the estimated covariance matrix.

The receiver identifies multipath components of the positioning signalsby generating a vector of sorted singular values, and using the vectorof sorted singular values to separate signal and noise subspaces,generating a noise subspace matrix, and estimating time of arrival of afirst path using the noise subspace matrix.

The receiver receives assistance data, wherein the assistance datacomprises at least one of system time at a rising edge of a pulse of awaveform, system time at a falling edge of a pulse of a waveform,geocode data of the plurality of transmitters, geocode data of adjacenttransmitters adjacent to the plurality of transmitters, index of asequence used by at least one transmitter in proximity of the pluralityof transmitters, clock timing corrections for at least one transmitter,local atmospheric corrections, relationship of WAPS timing to GNSS time,indication of local environment to aid the receiver in pseudorangeresolution, and at least one of an offset from base index of a set ofpseudorandom sequences, a list of pseudorandom number sequences from aset of transmitters, and a list of transmitters that utilize aparticular pseudorandom number sequence.

Embodiments described herein include a method for determining positioninformation using positioning signals transmitted from a plurality oftransmitters. The method comprises selecting a set of digitalpseudorandom sequences. Magnitudes of a cross-correlation functionbetween any two sequences of the set of digital pseudorandom sequencesare below a specified threshold. The method comprises selecting from theset of digital pseudorandom sequences a subset of digital pseudorandomsequences. The magnitudes of an autocorrelation function of each memberof the subset of digital pseudorandom sequences, within a specifiedregion adjacent to a peak of the autocorrelation function, are at leastone of equal to and less than a prescribed value. The method comprisestransmitting from each transmitter of the plurality of transmitters apositioning signal.

At least a first portion of the positioning signal is modulated inaccordance with at least one member of the subset of digitalpseudorandom sequences. At least two transmitters of the plurality oftransmitters modulate the first portion of respective positioningsignals in accordance with different members of the subset of digitalpseudorandom sequences. The method comprises receiving at a remotereceiver at least one of the positioning signals and satellite signals.The satellite signals are signals of a satellite-based positioningsystem. A first operating mode of the remote receiver comprisesterminal-based positioning in which the remote receiver computes aposition of the remote receiver from at least one of the positioningsignals and the satellite signals.

Embodiments described herein include a method for determining positioninformation using positioning signals transmitted from a plurality oftransmitters, comprising: selecting a set of digital pseudorandomsequences, wherein magnitudes of a cross-correlation function betweenany two sequences of the set of digital pseudorandom sequences are belowa specified threshold; selecting from the set of digital pseudorandomsequences a subset of digital pseudorandom sequences, wherein themagnitudes of an autocorrelation function of each member of the subsetof digital pseudorandom sequences, within a specified region adjacent toa peak of the autocorrelation function, are at least one of equal to andless than a prescribed value; transmitting from each transmitter of theplurality of transmitters a positioning signal, wherein at least a firstportion of the positioning signal is modulated in accordance with atleast one member of the subset of digital pseudorandom sequences,wherein at least two transmitters of the plurality of transmittersmodulate the first portion of respective positioning signals inaccordance with different members of the subset of digital pseudorandomsequences; and receiving at a remote receiver at least one of thepositioning signals and satellite signals, wherein the satellite signalsare signals of a satellite-based positioning system, wherein a firstoperating mode of the remote receiver comprises terminal-basedpositioning in which the remote receiver computes a position of theremote receiver from at least one of the positioning signals and thesatellite signals.

The set of digital pseudorandom sequences comprises a set of binarypseudorandom sequences.

The set of binary pseudorandom sequences is selected from a set of Goldcodes. The prescribed value is the peak value of the autocorrelationfunction divided by a non-repeating length of the digital pseudorandomsequence. The set of binary pseudorandom sequences is one of Kasamicodes, Bent codes, and Gold-like codes.

At least one digital pseudorandom sequence of the set of digitalpseudorandom sequences has a truncated sequence length, wherein thetruncated sequence length is shorter than a standard sequence length.Alternatively, at least one digital pseudorandom sequence of the set ofdigital pseudorandom sequences has an extended sequence length, whereinthe extended sequence length is longer than a standard sequence length.

The method comprises transmitting from at least one of the plurality oftransmitters a positioning signal during a first period of time forwhich the first portion of the positioning signal is modulated with afirst member of the subset of digital pseudorandom sequences, whereinthe first member of the subset of digital pseudorandom sequences has afirst length, and transmitting the positioning signal during a secondperiod of time for which a second portion of the positioning signal ismodulated with a second member of the subset of digital pseudorandomsequences, wherein the second member of the subset of digitalpseudorandom sequences has a second length.

The first length and the second length are different. The set of digitalpseudorandom sequences have an alphabet size greater than two (2).Theset of digital pseudorandom sequences is a set of quaternary sequences.The alphabet size is a power of two (2). The specified region adjacentto the peak of the autocorrelation function comprises at least ten (10)consecutive symbols immediately adjacent to the peak of theautocorrelation function.

A second portion of the positioning signal is further modulatedaccording to a data sequence.

A second operating mode of the remote receiver comprises network-basedpositioning in which a server computes a position of the remote receiverfrom information derived from at least one of the positioning signalsand the satellite signals, wherein the remote receiver receives andtransfers to the server information derived from at least one of thepositioning signals and the satellite signals.

Embodiments described herein include a positioning system. The systemcomprises a terrestrial transmitter network comprising a plurality oftransmitters that broadcast positioning signals and positioning data.The positioning data comprises data bits used to compute a distance to atransmitter broadcasting the positioning signals and the positioningdata. The plurality of transmitters selects a set of digitalpseudorandom sequences. Magnitudes of a cross-correlation functionbetween any two sequences of the set of digital pseudorandom sequencesare below a specified threshold. The plurality of transmitters selectsfrom the set of digital pseudorandom sequences a subset of digitalpseudorandom sequences. The magnitudes of an autocorrelation function ofeach member of the subset of digital pseudorandom sequences, within aspecified region adjacent to a peak of the autocorrelation function, areat least one of equal to and less than a prescribed value. For eachtransmitter at least a first portion of the positioning signal ismodulated with at least one member of the subset of digital pseudorandomsequences. At least two transmitters of the plurality of transmittersmodulate positioning signals with different members of the subset ofdigital pseudorandom sequences.

Embodiments described herein include a positioning system comprising: aterrestrial transmitter network comprising a plurality of transmittersthat broadcast positioning signals and positioning data, wherein thepositioning data comprises data bits used to compute a distance to atransmitter broadcasting the positioning signals and the positioningdata; wherein the plurality of transmitters select a set of digitalpseudorandom sequences, wherein magnitudes of a cross-correlationfunction between any two sequences of the set of digital pseudorandomsequences are below a specified threshold; wherein the plurality oftransmitters select from the set of digital pseudorandom sequences asubset of digital pseudorandom sequences, wherein the magnitudes of anautocorrelation function of each member of the subset of digitalpseudorandom sequences, within a specified region adjacent to a peak ofthe autocorrelation function, are at least one of equal to and less thana prescribed value; wherein for each transmitter at least a firstportion of the positioning signal is modulated with at least one memberof the subset of digital pseudorandom sequences, wherein at least twotransmitters of the plurality of transmitters modulate positioningsignals with different members of the subset of digital pseudorandomsequences.

The system comprises a remote receiver that acquires at least one of thepositioning signals and satellite signals, wherein the satellite signalsare signals of a satellite-based positioning system, wherein a firstoperating mode of the remote receiver comprises terminal-basedpositioning in which the remote receiver computes a position of theremote receiver from at least one of the positioning signals and thesatellite signals.

The system comprises a server coupled to the remote receiver, wherein asecond operating mode of the remote receiver comprises network-basedpositioning in which the server computes a position of the remotereceiver from information derived from at least one of the positioningsignals and the satellite signals, wherein the remote receiver receivesand transfers to the server information derived from at least one of thepositioning signals and the satellite signals.

The set of digital pseudorandom sequences comprises a set of binarypseudorandom sequences. The set of binary pseudorandom sequences isselected from a set of Gold codes. The prescribed value is the peakvalue of the autocorrelation function divided by a non-repeating lengthof the digital pseudorandom sequence. The set of binary pseudorandomsequences is one of Kasami codes, Bent codes, and Gold-like codes.

At least one digital pseudorandom sequence of the set of digitalpseudorandom sequences has a truncated sequence length, wherein thetruncated sequence length is shorter than a standard sequence length.Alternatively, at least one digital pseudorandom sequence of the set ofdigital pseudorandom sequences has an extended sequence length, whereinthe extended sequence length is longer than a standard sequence length.

The system comprises transmitting from at least one of the plurality oftransmitters a positioning signal during a first period of time forwhich the first portion of the positioning signal is modulated with afirst member of the subset of digital pseudorandom sequences, whereinthe first member of the subset of digital pseudorandom sequences has afirst length, and transmitting the positioning signal during a secondperiod of time for which a second portion of the positioning signal ismodulated with a second member of the subset of digital pseudorandomsequences, wherein the second member of the subset of digitalpseudorandom sequences has a second length.

The first length and the second length are different. The set of digitalpseudorandom sequences have an alphabet size greater than two (2). Theset of digital pseudorandom sequences is a set of quaternary sequences.The alphabet size is a power of two (2).

The specified region adjacent to the peak of the autocorrelationfunction comprises at least ten (10) consecutive symbols immediatelyadjacent to the peak of the autocorrelation function.

A first portion of the positioning signal is modulated with a member ofthe subset of digital pseudorandom sequences, and a second portion ofthe positioning signal is further modulated according to a data sequencecomprising the positioning data.

The system comprises a communication system coupled to at least one ofthe remote receiver and the plurality of transmitters, wherein thecommunication system is a cellular communication system. The pluralityof transmitters is synchronized.

Each transmitter of the plurality of transmitters transmits thepositioning data including assistance data, wherein the assistance datacomprises at least one of system time at an epoch of a waveform, geocodedata of the plurality of transmitters, geocode data of adjacenttransmitters adjacent to the plurality of transmitters, index of asequence used by at least one transmitter in proximity of the pluralityof transmitters, clock timing corrections for at least one transmitter,local atmospheric corrections, indication of local environment to aidthe remote receiver in pseudorange resolution, and at least one of anoffset from base index of the set of digital pseudorandom sequences, alist of digital pseudorandom sequences from a set of transmitters, and alist of transmitters that utilize a particular digital pseudorandomnumber sequence.

The signals transmitted by the plurality of transmitters comprise apreamble for at least one of frequency acquisition and timing alignment.The plurality of transmitters forms a CDMA network. Alternatively, theplurality of transmitters forms a TDMA network. A carrier signal of eachtransmitter is offset from at least one other carrier signal of othertransmitters of the plurality of transmitters.

The plurality of transmitters are positioned so that the remote receiverreceives signals from at least three transmitters and a geometricdilution of precision in each position is less than a threshold value,wherein the position of each of the plurality of transmitters isdetermined by minimizing a function that is a volume integration of asquare of the geometric dilution of precision over a coverage volume,wherein the volume integration is with respect to coordinates of aposition of the remote receiver, wherein the minimizing of the functionis with respect to transmitter position coordinates of transmitters ofthe plurality of transmitters in a specified coverage area in thecoverage volume, wherein the function is weighted according toperformance quality of a coverage region.

Each transmitter of the plurality of transmitters is synchronized to atime reference, and a timing correction of each transmitter is providedto the remote receiver. The remote receiver receives assistance datathat comprises at least one of system time at an epoch of a waveform,system time at a falling edge of a pulse of a waveform, geocode data ofthe plurality of transmitters, geocode data of transmitters adjacent tothe plurality of transmitters, index of a sequence used by at least onetransmitter in proximity of the plurality of transmitters, clock timingcorrections for at least one transmitter, local atmospheric corrections,indication of local environment to aid the remote receiver inpseudorange resolution, and at least one of an offset from base index ofthe set of digital pseudorandom sequences, a list of digitalpseudorandom sequences from a set of transmitters, and a list oftransmitters that utilize a particular digital pseudorandom numbersequence. The system comprises an atmospheric data sensor as a componentof the remote receiver, wherein at least one of the remote receiver andthe server compute a position of the remote receiver using data of theatmospheric data sensor, wherein the data of the atmospheric data sensorincludes at least one of pressure data, temperature data, and humiditydata. At least one of the remote receiver and the server compute a finalposition of the remote receiver using a range measurement from at leastone additional signal source combined with a range measurementdetermined using the positioning signals, wherein the final positioncomprises at least one of latitude, longitude and height. The componentsdescribed herein can be located together or in separate locations.Communication paths couple the components and include any medium forcommunicating or transferring files among the components. Thecommunication paths include wireless connections, wired connections, andhybrid wireless/wired connections. The communication paths also includecouplings or connections to networks including local area networks(LANs), metropolitan area networks (MANs), wide area networks (WANs),proprietary networks, interoffice or backend networks, and the Internet.Furthermore, the communication paths include removable fixed mediumslike floppy disks, hard disk drives, and CD-ROM disks, as well as flashRAM, Universal Serial Bus (USB) connections, RS-232 connections,telephone lines, buses, and electronic mail messages. Aspects of thesystems and methods described herein may be implemented as functionalityprogrammed into any of a variety of circuitry, including programmablelogic devices (PLDs), such as field programmable gate arrays (FPGAs),programmable array logic (PAL) devices, electrically programmable logicand memory devices and standard cell-based devices, as well asapplication specific integrated circuits (ASICs). Some otherpossibilities for implementing aspects of the systems and methodsinclude: microcontrollers with memory (such as electronically erasableprogrammable read only memory (EEPROM)), embedded microprocessors,firmware, software, etc. Furthermore, aspects of the systems and methodsmay be embodied in microprocessors having software-based circuitemulation, discrete logic (sequential and combinatorial), customdevices, fuzzy (neural) logic, quantum devices, and hybrids of any ofthe above device types. Of course the underlying device technologies maybe provided in a variety of component types, e.g., metal-oxidesemiconductor field-effect transistor (MOSFET) technologies likecomplementary metal-oxide semiconductor (CMOS), bipolar technologieslike emitter-coupled logic (ECL), polymer technologies (e.g.,silicon-conjugated polymer and metal-conjugated polymer-metalstructures), mixed analog and digital, etc. Unless the context clearlyrequires otherwise, throughout the description and the claims, the words“comprise,” “comprising,” and the like are to be construed in aninclusive sense as opposed to an exclusive or exhaustive sense; that isto say, in a sense of “including, but not limited to.” Words using thesingular or plural number also include the plural or singular numberrespectively. Additionally, the words “herein,” “hereunder,” “above,”“below,” and words of similar import, when used in this application,refer to this application as a whole and not to any particular portionsof this application. When the word “or” is used in reference to a listof two or more items, that word covers all of the followinginterpretations of the word: any of the items in the list, all of theitems in the list and any combination of the items in the list. Theabove description of embodiments of the systems and methods is notintended to be exhaustive or to limit the systems and methods to theprecise forms disclosed. While specific embodiments of, and examplesfor, the systems and methods are described herein for illustrativepurposes, various equivalent modifications are possible within the scopeof the systems and methods, as those skilled in the relevant art willrecognize. The teachings of the systems and methods provided herein canbe applied to other systems and methods, not only for the systems andmethods described above. The elements and acts of the variousembodiments described above can be combined to provide furtherembodiments. These and other changes can be made to the systems andmethods in light of the above detailed description. In general, in thefollowing claims, the terms used should not be construed to limit thesystems and methods to the specific embodiments disclosed in thespecification and the claims, but should be construed to include allsystems and methods that operate under the claims. Accordingly, thesystems and methods are not limited by the disclosure, but instead thescope is to be determined entirely by the claims. While certain aspectsof the systems and methods are presented below in certain claim forms,the inventors contemplate the various aspects of the systems and methodsin any number of claim forms. Accordingly, the inventors reserve theright to add additional claims after filing the application to pursuesuch additional claim forms for other aspects of the systems andmethods.

The contents of the following applications, which relate to the presentapplication, are hereby incorporated by reference herein in theirentirety: U.S. patent application Ser. No. 15/706,051, filed Sep. 15,2017; U.S. patent application Ser. No. 14/556,136, filed Nov. 29, 2014;U.S. patent application Ser. No. 13/535,626, filed Jun. 28, 2012; U.S.patent application Ser. No. 13/536,051, filed Jun. 28, 2012; U.S. PatentApplication 61/502,276, filed Jun. 28, 2011; and U.S. Patent Application61/502,272, filed Jun. 28, 2011.

1. A method for identifying pseudorandom sequences for use intransmitting signals from one or more transmitters to one or morereceivers, the method comprising: identifying a set of pseudorandomsequences, identifying a subset of at least three pseudorandom sequencesfrom the set of pseudorandom sequences, wherein more pseudorandomsequences are in the set of pseudorandom sequences than in the subset ofpseudorandom sequences; transmitting a first positioning signal, whereinat least a portion of the first positioning signal is modulated inaccordance with a first pseudorandom sequence from the subset ofpseudorandom sequences; and transmitting a second positioning signal,wherein at least a portion of the second positioning signal is modulatedin accordance with a second pseudorandom sequence from the subset ofpseudorandom sequences, wherein the second pseudorandom sequence and thefirst pseudorandom sequence are different pseudorandom sequences, andwherein the set and the subset are identified such that: (i) a magnitudeof a first autocorrelation function of each member of the set ofpseudorandom sequences, within a first region adjacent to a peak valueof the first autocorrelation function, is equal to or less than a firstprescribed value, and (ii) each magnitude of a first cross-correlationfunction between each pair of pseudorandom sequences in the subset isbelow a first specified threshold; or (i) a maximum magnitude of asecond cross-correlation function between any two pseudorandom sequencesof the set of pseudorandom sequences is below a second specifiedthreshold, and (ii) all magnitudes of a second autocorrelation functioncorresponding to the pseudorandom sequences of the subset, within asecond region adjacent to a peak value of the second autocorrelationfunction, are equal to or less than a second prescribed value.
 2. Themethod of claim 1, wherein the set and the subset are identified suchthat (i) the magnitude of the first autocorrelation function of eachmember of the set of pseudorandom sequences, within the first regionadjacent to the peak value of the first autocorrelation function, isequal to or less than the first prescribed value, and (ii) eachmagnitude of the first cross-correlation function between each pair ofpseudorandom sequences in the subset is below the first specifiedthreshold.
 3. The method of claim 2, wherein the first prescribed valueis less than or equal to a maximum magnitude of the cross-correlationfunction of any pair of pseudorandom sequences in the subset ofpseudorandom sequences, or wherein the first prescribed value is +/−1times the peak value of the first autocorrelation function divided by anon-repeating length of pseudorandom sequences in the subset.
 4. Themethod of claim 2, wherein a plurality of magnitudes of the firstautocorrelation function outside the first region exceed the firstprescribed value.
 5. The method of claim 2, wherein the first regionadjacent to the peak value of the first autocorrelation functionincludes at least five pseudorandom sequence symbols.
 6. The method ofclaim 2, wherein the magnitudes of the first cross-correlation functionare within a range of correlation offsets.
 7. The method of claim 1,wherein the set and the subset are identified such that (i) the maximummagnitude of the second cross-correlation function between any twopseudorandom sequences of the set of pseudorandom sequences is below thesecond specified threshold, and (ii) all magnitudes of the secondautocorrelation function corresponding to the pseudorandom sequences ofthe subset, within the second region adjacent to the peak value of thesecond autocorrelation function, are equal to or less than the secondprescribed value.
 8. The method of claim 7, wherein the secondprescribed value is less than or equal to the maximum magnitude of thesecond cross-correlation function between any two pseudorandom sequencesof the set of pseudorandom sequences, or wherein the second prescribedvalue is +/−1 times the peak value of the second autocorrelationfunction divided by a non-repeating length of pseudorandom sequences inthe subset.
 9. The method of claim 7, wherein two or more magnitudes ofthe second autocorrelation function, outside of the second region,exceed the second prescribed value.
 10. The method of claim 7, whereinthe second region adjacent to the peak of the second autocorrelationfunction includes at least five pseudorandom sequence symbols.
 11. Themethod of claim 7, wherein magnitudes of the second cross-correlationfunction between each pair of pseudorandom sequences in the subset arewithin a range of correlation offsets.
 12. The method of claim 1,wherein the set includes at least 176 pseudorandom sequences, whereinthe subset includes at least three pseudorandom sequences and no morethan ten pseudorandom sequences.
 13. The method of claim 1, wherein thefirst pseudorandom sequence includes a first set of phase angles used tophase modulate the first signal, and wherein the second pseudorandomsequence includes a second set of phase angles used to phase modulatethe second signal.
 14. The method of claim 1, wherein the pseudorandomsequences in the set have an alphabet size greater than two, wherein thealphabet size is a power of two.
 15. The method of claim 1, whereintransmitting a first positioning signal comprises transmitting the firstpositioning signal from a first transmitter, and wherein transmitting asecond positioning signal comprises transmitting the second positioningsignal from a second transmitter.
 16. The method of claim 1, whereintransmitting a first positioning signal comprises transmitting the firstpositioning signal from a first transmitter, and wherein transmitting asecond positioning signal comprises transmitting the second positioningsignal from the first transmitter.
 17. The method of claim 1, whereinthe first pseudorandom sequence has a first length, wherein the secondpseudorandom sequence pseudorandom sequence has a second length, andwherein the first length and the second length are different.
 18. Themethod of claim 1, wherein the first and second cross-correlationfunctions are circular cross-correlation functions, and wherein thefirst and second autocorrelation functions are circular autocorrelationfunctions.
 19. A non-transitory processor readable memory storingprogram instructions that, when executed by one or more processors,cause the one or more processors to implement the method of claim
 1. 20.A system comprising at least one processor that is operable to implementthe method of claim 1.